-16*x^2+86*x-108=0

Solution for -16*x^2+86*x-108=0 equation:

-16x^2+86x-108=0

a = -16; b = 86; c = -108;
Δ = b2-4ac
Δ = 862-4·(-16)·(-108)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-22}{2*-16}=\frac{-108}{-32}
=3+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+22}{2*-16}=\frac{-64}{-32}
=+2
$