5x2-32x-108=0

Solution for 5x2-32x-108=0 equation:

5x^2-32x-108=0

a = 5; b = -32; c = -108;
Δ = b2-4ac
Δ = -322-4·5·(-108)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{199}}{2*5}=\frac{32-4\sqrt{199}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{199}}{2*5}=\frac{32+4\sqrt{199}}{10}
$