12.6=X+0.1x^2

Solution for 12.6=X+0.1x^2 equation:

12.6=X+0.1X^2

We move all terms to the left:

12.6-(X+0.1X^2)=0

We get rid of parentheses

-0.1X^2-X+12.6=0

We add all the numbers together, and all the variables

-0.1X^2-1X+12.6=0

a = -0.1; b = -1; c = +12.6;
Δ = b2-4ac
Δ = -12-4·(-0.1)·12.6
Δ = 6.04
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{-(-1)-\sqrt{6.04}}{2*-0.1}=\frac{1-\sqrt{6.04}}{-0.2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6.04}}{2*-0.1}=\frac{1+\sqrt{6.04}}{-0.2}
$