4x^2-32x-72=0

Solution for 4x^2-32x-72=0 equation:

4x^2-32x-72=0

a = 4; b = -32; c = -72;
Δ = b2-4ac
Δ = -322-4·4·(-72)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{34}}{2*4}=\frac{32-8\sqrt{34}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{34}}{2*4}=\frac{32+8\sqrt{34}}{8}
$