6x^2+24x+24=96

Solution for 6x^2+24x+24=96 equation:

6x^2+24x+24=96

We move all terms to the left:

6x^2+24x+24-(96)=0

We add all the numbers together, and all the variables

6x^2+24x-72=0

a = 6; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·6·(-72)
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*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+48}{2*6}=\frac{24}{12}
=2
$