-0.8x^2-24x-90=0

Solution for -0.8x^2-24x-90=0 equation:

-0.8x^2-24x-90=0

a = -0.8; b = -24; c = -90;
Δ = b2-4ac
Δ = -242-4·(-0.8)·(-90)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{2}}{2*-0.8}=\frac{24-12\sqrt{2}}{-1.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{2}}{2*-0.8}=\frac{24+12\sqrt{2}}{-1.6}
$