A=-0.125x^2+2.25x-2

Solution for A=-0.125x^2+2.25x-2 equation:

=-0.125A^2+2.25A-2

We move all terms to the left:

-(-0.125A^2+2.25A-2)=0

We get rid of parentheses

0.125A^2-2.25A+2=0

a = 0.125; b = -2.25; c = +2;
Δ = b2-4ac
Δ = -2.252-4·0.125·2
Δ = 4.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.25)-\sqrt{4.0625}}{2*0.125}=\frac{2.25-\sqrt{4.0625}}{0.25}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.25)+\sqrt{4.0625}}{2*0.125}=\frac{2.25+\sqrt{4.0625}}{0.25}
$