x=12x^2+24x-96

Solution for x=12x^2+24x-96 equation:

x=12x^2+24x-96

We move all terms to the left:

x-(12x^2+24x-96)=0

We get rid of parentheses

-12x^2+x-24x+96=0

We add all the numbers together, and all the variables

-12x^2-23x+96=0

a = -12; b = -23; c = +96;
Δ = b2-4ac
Δ = -232-4·(-12)·96
Δ = 5137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{5137}}{2*-12}=\frac{23-\sqrt{5137}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{5137}}{2*-12}=\frac{23+\sqrt{5137}}{-24}
$