6x2=-12x-5

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

6x^2=-12x-5

We move all terms to the left:

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

We get rid of parentheses

6x^2+12x+5=0

a = 6; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·6·5
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*6}=\frac{-12-2\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{6}}{2*6}=\frac{-12+2\sqrt{6}}{12}
$