3x(x+24)=90

Solution for 3x(x+24)=90 equation:

3x(x+24)=90

We move all terms to the left:

3x(x+24)-(90)=0

We multiply parentheses

3x^2+72x-90=0

a = 3; b = 72; c = -90;
Δ = b2-4ac
Δ = 722-4·3·(-90)
Δ = 6264
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:

$\sqrt{\Delta}=\sqrt{6264}=\sqrt{36*174}=\sqrt{36}*\sqrt{174}=6\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{174}}{2*3}=\frac{-72-6\sqrt{174}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{174}}{2*3}=\frac{-72+6\sqrt{174}}{6}
$