2x+2x^2=56

Solution for 2x+2x^2=56 equation:

2x+2x^2=56

We move all terms to the left:

2x+2x^2-(56)=0

a = 2; b = 2; c = -56;
Δ = b2-4ac
Δ = 22-4·2·(-56)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{113}}{2*2}=\frac{-2-2\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{113}}{2*2}=\frac{-2+2\sqrt{113}}{4}
$