-2x^2-48x+86=0

Solution for -2x^2-48x+86=0 equation:

-2x^2-48x+86=0

a = -2; b = -48; c = +86;
Δ = b2-4ac
Δ = -482-4·(-2)·86
Δ = 2992
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:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{187}}{2*-2}=\frac{48-4\sqrt{187}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{187}}{2*-2}=\frac{48+4\sqrt{187}}{-4}
$