8a-2=12+a2

Solution for 8a-2=12+a2 equation:

8a-2=12+a2

We move all terms to the left:

8a-2-(12+a2)=0

We add all the numbers together, and all the variables

-(+a^2+12)+8a-2=0

We get rid of parentheses

-a^2+8a-12-2=0

We add all the numbers together, and all the variables

-1a^2+8a-14=0

a = -1; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·(-1)·(-14)
Δ = 8
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:

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