9=0.0002x^2-0.316x+127.9

Solution for 9=0.0002x^2-0.316x+127.9 equation:

9=0.0002x^2-0.316x+127.9

We move all terms to the left:

9-(0.0002x^2-0.316x+127.9)=0

We get rid of parentheses

-0.0002x^2+0.316x-127.9+9=0

We add all the numbers together, and all the variables

-0.0002x^2+0.316x-118.9=0

a = -0.0002; b = 0.316; c = -118.9;
Δ = b2-4ac
Δ = 0.3162-4·(-0.0002)·(-118.9)
Δ = 0.004736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.316)-\sqrt{0.004736}}{2*-0.0002}=\frac{-0.316-\sqrt{0.004736}}{-0.0004}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.316)+\sqrt{0.004736}}{2*-0.0002}=\frac{-0.316+\sqrt{0.004736}}{-0.0004}
$