x^2-36x+120=0

Solution for x^2-36x+120=0 equation:

x^2-36x+120=0

a = 1; b = -36; c = +120;
Δ = b2-4ac
Δ = -362-4·1·120
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{51}}{2*1}=\frac{36-4\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{51}}{2*1}=\frac{36+4\sqrt{51}}{2}
$