-2x^2-8x+7=0

Solution for -2x^2-8x+7=0 equation:

-2x^2-8x+7=0

a = -2; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-2)·7
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{30}}{2*-2}=\frac{8-2\sqrt{30}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{30}}{2*-2}=\frac{8+2\sqrt{30}}{-4}
$