4x^2-52x-128=0

Solution for 4x^2-52x-128=0 equation:

4x^2-52x-128=0

a = 4; b = -52; c = -128;
Δ = b2-4ac
Δ = -522-4·4·(-128)
Δ = 4752
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:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{33}}{2*4}=\frac{52-12\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{33}}{2*4}=\frac{52+12\sqrt{33}}{8}
$