8x2+8x=14

Solution for 8x2+8x=14 equation:

8x^2+8x=14

We move all terms to the left:

8x^2+8x-(14)=0

a = 8; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·8·(-14)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{2}}{2*8}=\frac{-8-16\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{2}}{2*8}=\frac{-8+16\sqrt{2}}{16}
$