310=2x^2+24x

Solution for 310=2x^2+24x equation:

310=2x^2+24x

We move all terms to the left:

310-(2x^2+24x)=0

We get rid of parentheses

-2x^2-24x+310=0

a = -2; b = -24; c = +310;
Δ = b2-4ac
Δ = -242-4·(-2)·310
Δ = 3056
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:

$\sqrt{\Delta}=\sqrt{3056}=\sqrt{16*191}=\sqrt{16}*\sqrt{191}=4\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{191}}{2*-2}=\frac{24-4\sqrt{191}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{191}}{2*-2}=\frac{24+4\sqrt{191}}{-4}
$