-2x^2-39x-54=0

Solution for -2x^2-39x-54=0 equation:

-2x^2-39x-54=0

a = -2; b = -39; c = -54;
Δ = b2-4ac
Δ = -392-4·(-2)·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-33}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+33}{2*-2}=\frac{72}{-4}
=-18
$