4x^2=24x+108

Solution for 4x^2=24x+108 equation:

4x^2=24x+108

We move all terms to the left:

4x^2-(24x+108)=0

We get rid of parentheses

4x^2-24x-108=0

a = 4; b = -24; c = -108;
Δ = b2-4ac
Δ = -242-4·4·(-108)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-48}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*4}=\frac{72}{8}
=9
$