-16x^2+108x-25=0

Solution for -16x^2+108x-25=0 equation:

-16x^2+108x-25=0

a = -16; b = 108; c = -25;
Δ = b2-4ac
Δ = 1082-4·(-16)·(-25)
Δ = 10064
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:

$\sqrt{\Delta}=\sqrt{10064}=\sqrt{16*629}=\sqrt{16}*\sqrt{629}=4\sqrt{629}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{629}}{2*-16}=\frac{-108-4\sqrt{629}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{629}}{2*-16}=\frac{-108+4\sqrt{629}}{-32}
$