-0.01x^2-0.2x+23=8

Solution for -0.01x^2-0.2x+23=8 equation:

-0.01x^2-0.2x+23=8

We move all terms to the left:

-0.01x^2-0.2x+23-(8)=0

We add all the numbers together, and all the variables

-0.01x^2-0.2x+15=0

a = -0.01; b = -0.2; c = +15;
Δ = b2-4ac
Δ = -0.22-4·(-0.01)·15
Δ = 0.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-\sqrt{0.64}}{2*-0.01}=\frac{0.2-\sqrt{0.64}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{0.64}}{2*-0.01}=\frac{0.2+\sqrt{0.64}}{-0.02}
$