x(x-4)=90

Solution for x(x-4)=90 equation:

x(x-4)=90

We move all terms to the left:

x(x-4)-(90)=0

We multiply parentheses

x^2-4x-90=0

a = 1; b = -4; c = -90;
Δ = b2-4ac
Δ = -42-4·1·(-90)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*1}=\frac{4-2\sqrt{94}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*1}=\frac{4+2\sqrt{94}}{2}
$