(X-90)x=20

Solution for (X-90)x=20 equation:

(X-90)X=20

We move all terms to the left:

(X-90)X-(20)=0

We multiply parentheses

X^2-90X-20=0

a = 1; b = -90; c = -20;
Δ = b2-4ac
Δ = -902-4·1·(-20)
Δ = 8180
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:

$\sqrt{\Delta}=\sqrt{8180}=\sqrt{4*2045}=\sqrt{4}*\sqrt{2045}=2\sqrt{2045}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2045}}{2*1}=\frac{90-2\sqrt{2045}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2045}}{2*1}=\frac{90+2\sqrt{2045}}{2}
$