(x-18)x=90

Solution for (x-18)x=90 equation:

(x-18)x=90

We move all terms to the left:

(x-18)x-(90)=0

We multiply parentheses

x^2-18x-90=0

a = 1; b = -18; c = -90;
Δ = b2-4ac
Δ = -182-4·1·(-90)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{19}}{2*1}=\frac{18-6\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{19}}{2*1}=\frac{18+6\sqrt{19}}{2}
$