x(x-36)=90

Solution for x(x-36)=90 equation:

x(x-36)=90

We move all terms to the left:

x(x-36)-(90)=0

We multiply parentheses

x^2-36x-90=0

a = 1; b = -36; c = -90;
Δ = b2-4ac
Δ = -362-4·1·(-90)
Δ = 1656
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:

$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{46}}{2*1}=\frac{36-6\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{46}}{2*1}=\frac{36+6\sqrt{46}}{2}
$