-0.8x^2-12x-22.5=0

Solution for -0.8x^2-12x-22.5=0 equation:

-0.8x^2-12x-22.5=0

a = -0.8; b = -12; c = -22.5;
Δ = b2-4ac
Δ = -122-4·(-0.8)·(-22.5)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*-0.8}=\frac{12-6\sqrt{2}}{-1.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*-0.8}=\frac{12+6\sqrt{2}}{-1.6}
$