-16(x^2)+112(x)+84=0

Solution for -16(x^2)+112(x)+84=0 equation:

-16(x^2)+112(x)+84=0

a = -16; b = 112; c = +84;
Δ = b2-4ac
Δ = 1122-4·(-16)·84
Δ = 17920
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:

$\sqrt{\Delta}=\sqrt{17920}=\sqrt{256*70}=\sqrt{256}*\sqrt{70}=16\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-16\sqrt{70}}{2*-16}=\frac{-112-16\sqrt{70}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+16\sqrt{70}}{2*-16}=\frac{-112+16\sqrt{70}}{-32}
$