x(x-9)=90

Solution for x(x-9)=90 equation:

x(x-9)=90

We move all terms to the left:

x(x-9)-(90)=0

We multiply parentheses

x^2-9x-90=0

a = 1; b = -9; c = -90;
Δ = b2-4ac
Δ = -92-4·1·(-90)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*1}=\frac{30}{2}
=15
$