-2x^2-8x+76=0

Solution for -2x^2-8x+76=0 equation:

-2x^2-8x+76=0

a = -2; b = -8; c = +76;
Δ = b2-4ac
Δ = -82-4·(-2)·76
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{42}}{2*-2}=\frac{8-4\sqrt{42}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{42}}{2*-2}=\frac{8+4\sqrt{42}}{-4}
$