4x^2-80x-32=0

Solution for 4x^2-80x-32=0 equation:

4x^2-80x-32=0

a = 4; b = -80; c = -32;
Δ = b2-4ac
Δ = -802-4·4·(-32)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-48\sqrt{3}}{2*4}=\frac{80-48\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+48\sqrt{3}}{2*4}=\frac{80+48\sqrt{3}}{8}
$