-16x^2+116x-108=0

Solution for -16x^2+116x-108=0 equation:

-16x^2+116x-108=0

a = -16; b = 116; c = -108;
Δ = b2-4ac
Δ = 1162-4·(-16)·(-108)
Δ = 6544
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:

$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-4\sqrt{409}}{2*-16}=\frac{-116-4\sqrt{409}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+4\sqrt{409}}{2*-16}=\frac{-116+4\sqrt{409}}{-32}
$