X(x-32)=90

Solution for X(x-32)=90 equation:

X(X-32)=90

We move all terms to the left:

X(X-32)-(90)=0

We multiply parentheses

X^2-32X-90=0

a = 1; b = -32; c = -90;
Δ = b2-4ac
Δ = -322-4·1·(-90)
Δ = 1384
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:

$\sqrt{\Delta}=\sqrt{1384}=\sqrt{4*346}=\sqrt{4}*\sqrt{346}=2\sqrt{346}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{346}}{2*1}=\frac{32-2\sqrt{346}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{346}}{2*1}=\frac{32+2\sqrt{346}}{2}
$