X-x(x-90)=18

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

X-X(X-90)=18

We move all terms to the left:

X-X(X-90)-(18)=0

We multiply parentheses

-X^2+X+90X-18=0

We add all the numbers together, and all the variables

-1X^2+91X-18=0

a = -1; b = 91; c = -18;
Δ = b2-4ac
Δ = 912-4·(-1)·(-18)
Δ = 8209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-\sqrt{8209}}{2*-1}=\frac{-91-\sqrt{8209}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{8209}}{2*-1}=\frac{-91+\sqrt{8209}}{-2}
$