-4x^2-48x-20=0

Solution for -4x^2-48x-20=0 equation:

-4x^2-48x-20=0

a = -4; b = -48; c = -20;
Δ = b2-4ac
Δ = -482-4·(-4)·(-20)
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{31}}{2*-4}=\frac{48-8\sqrt{31}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{31}}{2*-4}=\frac{48+8\sqrt{31}}{-8}
$