Possible Safe Areas In a Solar Flare Which part of the earth would be the safest in case of the major solar flare?
Will it be near equator or something like that?
 A: Just to confirm that CuriousOne is correct as regards direct radiation damage to your body.
From Solar Flares

Solar flares are gigantic explosions associated with sunspots, caused by the sudden release of energy from “twists” in the sun’s magnetic field. They are intense bursts of radiation that can last for anywhere from minutes to hours. Solar flares and CMEs pose no direct threat to humans—Earth’s atmosphere protects us from the radiation of space weather. (If an astronaut out in space is bombarded with the high-energy particles from a CME, he or she could be seriously injured or killed. But most of us won’t have to worry about that situation.) We could, however, feel the effects of CMEs indirectly, through the disruptions to our technology—some of which could have devastating and lingering effects on civilization.

As an example of this, you could read Quebec Blackout and as we become more reliant on satellites, we spend a lot of effort hardening their electronic components against radiation.  We also try to predict Solar weather, so we can turn things off before the flare affects us.
However, taking into account what I have learned from @RobJefferies comments below, your best chance of minimising indirect effects are, as you say in your post, near the equator. 
A: Clarifications
There is a difference between a solar flare and a the phenomena that cause things like the 1989 Quebec blackout and/or the 1970s New York blackout (I think it was 1972 but do not recall off hand).  The latter phenomena are called coronal mass ejections (CMEs) because they actually involve large amounts (i.e., upwards of billions of tons) of matter (in the form of plasma) to leave the sun.
A solar flare is really described by the sudden enhancement of x-rays from a small region in the solar corona.  They can produce streams of high energy particles, called solar energetic particles or SEPs (CMEs can produce SEPs as well), but these are streams of magnetic field-aligned particles propagating away from the sun.  They can have energies up to ~GeV for ions and several ~MeV for electrons, but rarely higher.  Earth's atmosphere does a great job of shielding much of this and the surrounding magnetic field helps to "deflect" some of the incident particles as well.
A CME, on the other hand, expands nearly as fast as it propagates which means their radius of curvature by the time they reach Earth is nearly 1 AU.  They are, in effect, a large "magnetic piston" (sometimes called a magnetic cloud or flux rope etc.) that piles-up plasma on their leading edge and can produce rather strong collisionless shock waves.  The magnetic field orientation of the magnetic piston is very important, as its orientation relative to the Earth's magnetic field can result in either a small auroral response or a major geomagnetic storm.

Which part of the earth would be the safest in case of the major solar flare?

As for avoiding electrical blackouts due to ground induced currents, lower latitudes are the best option (i.e., near the geographic equator... at least for now).  Generally, higher latitudes are more strongly affected by geomagnetic disturbances.  I wrote a more detailed answer regarding how the Earth is affected at https://physics.stackexchange.com/a/214509/59023.
I wrote another answer to a similar question at https://physics.stackexchange.com/a/149199/59023 that explains the low probability of any physical harm coming to any individual or even most power grids.  The way most grids are assembled and operated, if any major transformer were to fail it typically causes the whole grid to shutdown and restart, which would prevent (or at least slow) the demise of other transformers.  So most power grids are not in tremendous danger, but that is no reason to be lazy or careless about such things.  We have not had a Carrington-like event since at least the 1970s, so it is unclear how some of our newer electronic systems may respond.
What about spacecraft or astronauts?
Spacecraft (SC) suffer from several effects that are directly caused by either solar flares and/or CMEs.  Since SC are not connected to the Earth, they have no effective electrical ground so they can charge up, as discussed in this arXiv 0906.3884 paper.  When exposed to sunlight, they often charge positive because the emission of photoelectrons typically dominates over the thermal currents from the background electron plasma.  However, if the SC is, say, behind the Earth then it can charge negative.
During strong geomagnetic storms there are large inflows of high energy particles from the geomagnetic tail.  The smaller gyroradii and higher thermal speeds results in a larger fraction of the electrons than ions striking a SC in the Earth's shadow.  The result is the SC can become very negatively charged, in some cases to several kilovolts.  There have been reports of electrical arcing resulting from such high charges combined with the numerous sharp edges on many SC buses.  It is still debated (for insurance, not science reasons) whether any spacecraft have been "killed" by such charging events.
As for astronauts, they could be in trouble.  The Earth's radiation belts also enhance during geomagnetic storms and the international space station (ISS) often goes through regions of the inner belt.  During strong storms, much of the ISS's orbit can be enveloped in the inner belt, which is primarily composed of protons with energies up to >100 MeV.  The shielding on the ISS is made for protons generally below ~50 MeV, but discussing radiation doses could fill several more pages.
Astronauts are also exposed, if on the dayside, to the SEPs I mentioned earlier.  Those can be up to ~GeV and can also be made of neutrons, which can be worse in several ways (radiation-wise).  So the astronauts are generally exposed to a great deal more radiation than anyone staying on Earth (except perhaps people working near radioactive materials).
