2x(x+24)=90

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

2x(x+24)=90

We move all terms to the left:

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

We multiply parentheses

2x^2+48x-90=0

a = 2; b = 48; c = -90;
Δ = b2-4ac
Δ = 482-4·2·(-90)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{21}}{2*2}=\frac{-48-12\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{21}}{2*2}=\frac{-48+12\sqrt{21}}{4}
$