-x^2-48x-68=0

Solution for -x^2-48x-68=0 equation:

-x^2-48x-68=0

We add all the numbers together, and all the variables

-1x^2-48x-68=0

a = -1; b = -48; c = -68;
Δ = b2-4ac
Δ = -482-4·(-1)·(-68)
Δ = 2032
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:

$\sqrt{\Delta}=\sqrt{2032}=\sqrt{16*127}=\sqrt{16}*\sqrt{127}=4\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{127}}{2*-1}=\frac{48-4\sqrt{127}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{127}}{2*-1}=\frac{48+4\sqrt{127}}{-2}
$