6x^2=-24x-18

Solution for 6x^2=-24x-18 equation:

6x^2=-24x-18

We move all terms to the left:

6x^2-(-24x-18)=0

We get rid of parentheses

6x^2+24x+18=0

a = 6; b = 24; c = +18;
Δ = b2-4ac
Δ = 242-4·6·18
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*6}=\frac{-12}{12}
=-1
$