X^2-64x-180=0

Solution for X^2-64x-180=0 equation:

X^2-64X-180=0

a = 1; b = -64; c = -180;
Δ = b2-4ac
Δ = -642-4·1·(-180)
Δ = 4816
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:

$\sqrt{\Delta}=\sqrt{4816}=\sqrt{16*301}=\sqrt{16}*\sqrt{301}=4\sqrt{301}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{301}}{2*1}=\frac{64-4\sqrt{301}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{301}}{2*1}=\frac{64+4\sqrt{301}}{2}
$