-.8x^2+24x-90=0

Solution for -.8x^2+24x-90=0 equation:

-.8x^2+24x-90=0

We add all the numbers together, and all the variables

-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}
$