5x^2-6=-6x

Solution for 5x^2-6=-6x equation:

5x^2-6=-6x

We move all terms to the left:

5x^2-6-(-6x)=0

We get rid of parentheses

5x^2+6x-6=0

a = 5; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·5·(-6)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*5}=\frac{-6-2\sqrt{39}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*5}=\frac{-6+2\sqrt{39}}{10}
$