12.5=5.2x+9.81x^2

Solution for 12.5=5.2x+9.81x^2 equation:

12.5=5.2x+9.81x^2

We move all terms to the left:

12.5-(5.2x+9.81x^2)=0

We get rid of parentheses

-9.81x^2-5.2x+12.5=0

a = -9.81; b = -5.2; c = +12.5;
Δ = b2-4ac
Δ = -5.22-4·(-9.81)·12.5
Δ = 517.54
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{-(-5.2)-\sqrt{517.54}}{2*-9.81}=\frac{5.2-\sqrt{517.54}}{-19.62}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.2)+\sqrt{517.54}}{2*-9.81}=\frac{5.2+\sqrt{517.54}}{-19.62}
$