4(x+4)(x-7)=96

Solution for 4(x+4)(x-7)=96 equation:

4(x+4)(x-7)=96

We move all terms to the left:

4(x+4)(x-7)-(96)=0

We multiply parentheses ..

4(+x^2-7x+4x-28)-96=0

We multiply parentheses

4x^2-28x+16x-112-96=0

We add all the numbers together, and all the variables

4x^2-12x-208=0

a = 4; b = -12; c = -208;
Δ = b2-4ac
Δ = -122-4·4·(-208)
Δ = 3472
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:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{217}}{2*4}=\frac{12-4\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{217}}{2*4}=\frac{12+4\sqrt{217}}{8}
$