X^2-52x-164=0

Solution for X^2-52x-164=0 equation:

X^2-52X-164=0

a = 1; b = -52; c = -164;
Δ = b2-4ac
Δ = -522-4·1·(-164)
Δ = 3360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{210}}{2*1}=\frac{52-4\sqrt{210}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{210}}{2*1}=\frac{52+4\sqrt{210}}{2}
$