3x^2+18x+13=-2

Solution for 3x^2+18x+13=-2 equation:

3x^2+18x+13=-2

We move all terms to the left:

3x^2+18x+13-(-2)=0

We add all the numbers together, and all the variables

3x^2+18x+15=0

a = 3; b = 18; c = +15;
Δ = b2-4ac
Δ = 182-4·3·15
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{-(18)-12}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*3}=\frac{-6}{6}
=-1
$