6a^2-10=-6a

Solution for 6a^2-10=-6a equation:

6a^2-10=-6a

We move all terms to the left:

6a^2-10-(-6a)=0

We get rid of parentheses

6a^2+6a-10=0

a = 6; b = 6; c = -10;
Δ = b2-4ac
Δ = 62-4·6·(-10)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*6}=\frac{-6-2\sqrt{69}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*6}=\frac{-6+2\sqrt{69}}{12}
$