-16x^2+112x-125=0

Solution for -16x^2+112x-125=0 equation:

-16x^2+112x-125=0

a = -16; b = 112; c = -125;
Δ = b2-4ac
Δ = 1122-4·(-16)·(-125)
Δ = 4544
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:

$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-8\sqrt{71}}{2*-16}=\frac{-112-8\sqrt{71}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+8\sqrt{71}}{2*-16}=\frac{-112+8\sqrt{71}}{-32}
$