127=0.006a^2-0.02a+120

Solution for 127=0.006a^2-0.02a+120 equation:

127=0.006a^2-0.02a+120

We move all terms to the left:

127-(0.006a^2-0.02a+120)=0

We get rid of parentheses

-0.006a^2+0.02a-120+127=0

We add all the numbers together, and all the variables

-0.006a^2+0.02a+7=0

a = -0.006; b = 0.02; c = +7;
Δ = b2-4ac
Δ = 0.022-4·(-0.006)·7
Δ = 0.1684
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{-(0.02)-\sqrt{0.1684}}{2*-0.006}=\frac{-0.02-\sqrt{0.1684}}{-0.012}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.02)+\sqrt{0.1684}}{2*-0.006}=\frac{-0.02+\sqrt{0.1684}}{-0.012}
$