31=2x^2+16x

Solution for 31=2x^2+16x equation:

31=2x^2+16x

We move all terms to the left:

31-(2x^2+16x)=0

We get rid of parentheses

-2x^2-16x+31=0

a = -2; b = -16; c = +31;
Δ = b2-4ac
Δ = -162-4·(-2)·31
Δ = 504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{14}}{2*-2}=\frac{16-6\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{14}}{2*-2}=\frac{16+6\sqrt{14}}{-4}
$