3x^2+18x=-2

Solution for 3x^2+18x=-2 equation:

3x^2+18x=-2

We move all terms to the left:

3x^2+18x-(-2)=0

We add all the numbers together, and all the variables

3x^2+18x+2=0

a = 3; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·3·2
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{3}}{2*3}=\frac{-18-10\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{3}}{2*3}=\frac{-18+10\sqrt{3}}{6}
$