5x2=-12x-6

Solution for 5x2=-12x-6 equation:

5x^2=-12x-6

We move all terms to the left:

5x^2-(-12x-6)=0

We get rid of parentheses

5x^2+12x+6=0

a = 5; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·5·6
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{6}}{2*5}=\frac{-12-2\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{6}}{2*5}=\frac{-12+2\sqrt{6}}{10}
$