31=11.6x+4.905x^2

Solution for 31=11.6x+4.905x^2 equation:

31=11.6x+4.905x^2

We move all terms to the left:

31-(11.6x+4.905x^2)=0

We get rid of parentheses

-4.905x^2-11.6x+31=0

a = -4.905; b = -11.6; c = +31;
Δ = b2-4ac
Δ = -11.62-4·(-4.905)·31
Δ = 742.78
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{-(-11.6)-\sqrt{742.78}}{2*-4.905}=\frac{11.6-\sqrt{742.78}}{-9.81}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.6)+\sqrt{742.78}}{2*-4.905}=\frac{11.6+\sqrt{742.78}}{-9.81}
$