-16x^2+82x-68=0

Solution for -16x^2+82x-68=0 equation:

-16x^2+82x-68=0

a = -16; b = 82; c = -68;
Δ = b2-4ac
Δ = 822-4·(-16)·(-68)
Δ = 2372
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:

$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{593}}{2*-16}=\frac{-82-2\sqrt{593}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{593}}{2*-16}=\frac{-82+2\sqrt{593}}{-32}
$