-.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 = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*-0.8}=\frac{24-12\sqrt{6}}{-1.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*-0.8}=\frac{24+12\sqrt{6}}{-1.6}
$