2x+x(x-24)=90

Solution for 2x+x(x-24)=90 equation:

2x+x(x-24)=90

We move all terms to the left:

2x+x(x-24)-(90)=0

We multiply parentheses

x^2+2x-24x-90=0

We add all the numbers together, and all the variables

x^2-22x-90=0

a = 1; b = -22; c = -90;
Δ = b2-4ac
Δ = -222-4·1·(-90)
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{211}}{2*1}=\frac{22-2\sqrt{211}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{211}}{2*1}=\frac{22+2\sqrt{211}}{2}
$