140=0.01a^2+0.05a+107

Solution for 140=0.01a^2+0.05a+107 equation:

140=0.01a^2+0.05a+107

We move all terms to the left:

140-(0.01a^2+0.05a+107)=0

We get rid of parentheses

-0.01a^2-0.05a-107+140=0

We add all the numbers together, and all the variables

-0.01a^2-0.05a+33=0

a = -0.01; b = -0.05; c = +33;
Δ = b2-4ac
Δ = -0.052-4·(-0.01)·33
Δ = 1.3225
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{1.3225}}{2*-0.01}=\frac{0.05-\sqrt{1.3225}}{-0.02}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{1.3225}}{2*-0.01}=\frac{0.05+\sqrt{1.3225}}{-0.02}
$