x^2-64x+120=0

Solution for x^2-64x+120=0 equation:

x^2-64x+120=0

a = 1; b = -64; c = +120;
Δ = b2-4ac
Δ = -642-4·1·120
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{226}}{2*1}=\frac{64-4\sqrt{226}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{226}}{2*1}=\frac{64+4\sqrt{226}}{2}
$