8a^2+8a=-5+14

Solution for 8a^2+8a=-5+14 equation:

8a^2+8a=-5+14

We move all terms to the left:

8a^2+8a-(-5+14)=0

We add all the numbers together, and all the variables

8a^2+8a-9=0

a = 8; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·8·(-9)
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*8}=\frac{-8-4\sqrt{22}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*8}=\frac{-8+4\sqrt{22}}{16}
$