8a^2+2=9a^2-12a-2

Solution for 8a^2+2=9a^2-12a-2 equation:

8a^2+2=9a^2-12a-2

We move all terms to the left:

8a^2+2-(9a^2-12a-2)=0

We get rid of parentheses

8a^2-9a^2+12a+2+2=0

We add all the numbers together, and all the variables

-1a^2+12a+4=0

a = -1; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-1)·4
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*-1}=\frac{-12-4\sqrt{10}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*-1}=\frac{-12+4\sqrt{10}}{-2}
$