-16x^2+82x+7=0

Solution for -16x^2+82x+7=0 equation:

-16x^2+82x+7=0

a = -16; b = 82; c = +7;
Δ = b2-4ac
Δ = 822-4·(-16)·7
Δ = 7172
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:

$\sqrt{\Delta}=\sqrt{7172}=\sqrt{4*1793}=\sqrt{4}*\sqrt{1793}=2\sqrt{1793}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{1793}}{2*-16}=\frac{-82-2\sqrt{1793}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{1793}}{2*-16}=\frac{-82+2\sqrt{1793}}{-32}
$