6x^2+24x=-10

Solution for 6x^2+24x=-10 equation:

6x^2+24x=-10

We move all terms to the left:

6x^2+24x-(-10)=0

We add all the numbers together, and all the variables

6x^2+24x+10=0

a = 6; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·6·10
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{21}}{2*6}=\frac{-24-4\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{21}}{2*6}=\frac{-24+4\sqrt{21}}{12}
$