114=2x^2+8x

Solution for 114=2x^2+8x equation:

114=2x^2+8x

We move all terms to the left:

114-(2x^2+8x)=0

We get rid of parentheses

-2x^2-8x+114=0

a = -2; b = -8; c = +114;
Δ = b2-4ac
Δ = -82-4·(-2)·114
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{61}}{2*-2}=\frac{8-4\sqrt{61}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{61}}{2*-2}=\frac{8+4\sqrt{61}}{-4}
$