-16x^2+192x+7=0

Solution for -16x^2+192x+7=0 equation:

-16x^2+192x+7=0

a = -16; b = 192; c = +7;
Δ = b2-4ac
Δ = 1922-4·(-16)·7
Δ = 37312
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:

$\sqrt{\Delta}=\sqrt{37312}=\sqrt{64*583}=\sqrt{64}*\sqrt{583}=8\sqrt{583}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-8\sqrt{583}}{2*-16}=\frac{-192-8\sqrt{583}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+8\sqrt{583}}{2*-16}=\frac{-192+8\sqrt{583}}{-32}
$