8n^2-2=6n+6

Solution for 8n^2-2=6n+6 equation:

8n^2-2=6n+6

We move all terms to the left:

8n^2-2-(6n+6)=0

We get rid of parentheses

8n^2-6n-6-2=0

We add all the numbers together, and all the variables

8n^2-6n-8=0

a = 8; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·8·(-8)
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{73}}{2*8}=\frac{6-2\sqrt{73}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{73}}{2*8}=\frac{6+2\sqrt{73}}{16}
$