4x^2+20x-96^2=0

Solution for 4x^2+20x-96^2=0 equation:

4x^2+20x-96^2=0

We add all the numbers together, and all the variables

4x^2+20x-9216=0

a = 4; b = 20; c = -9216;
Δ = b2-4ac
Δ = 202-4·4·(-9216)
Δ = 147856
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:

$\sqrt{\Delta}=\sqrt{147856}=\sqrt{16*9241}=\sqrt{16}*\sqrt{9241}=4\sqrt{9241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{9241}}{2*4}=\frac{-20-4\sqrt{9241}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{9241}}{2*4}=\frac{-20+4\sqrt{9241}}{8}
$