-5x^2-90x-400=0

Solution for -5x^2-90x-400=0 equation:

-5x^2-90x-400=0

a = -5; b = -90; c = -400;
Δ = b2-4ac
Δ = -902-4·(-5)·(-400)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10}{2*-5}=\frac{80}{-10}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10}{2*-5}=\frac{100}{-10}
=-10
$