125=0.01(a^2)+0.05a+107

Solution for 125=0.01(a^2)+0.05a+107 equation:

125=0.01(a^2)+0.05a+107

We move all terms to the left:

125-(0.01(a^2)+0.05a+107)=0

We get rid of parentheses

-0.01a^2-0.05a-107+125=0

We add all the numbers together, and all the variables

-0.01a^2-0.05a+18=0

a = -0.01; b = -0.05; c = +18;
Δ = b2-4ac
Δ = -0.052-4·(-0.01)·18
Δ = 0.7225
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{-(-0.05)-\sqrt{0.7225}}{2*-0.01}=\frac{0.05-\sqrt{0.7225}}{-0.02}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{0.7225}}{2*-0.01}=\frac{0.05+\sqrt{0.7225}}{-0.02}
$