A=-0.125x^2+2.25x+1

Solution for A=-0.125x^2+2.25x+1 equation:

=-0.125A^2+2.25A+1

We move all terms to the left:

-(-0.125A^2+2.25A+1)=0

We get rid of parentheses

0.125A^2-2.25A-1=0

a = 0.125; b = -2.25; c = -1;
Δ = b2-4ac
Δ = -2.252-4·0.125·(-1)
Δ = 5.5625
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{5.5625}}{2*0.125}=\frac{2.25-\sqrt{5.5625}}{0.25}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.25)+\sqrt{5.5625}}{2*0.125}=\frac{2.25+\sqrt{5.5625}}{0.25}
$