6x^2+27x+15=-2x^2-3x-13

Solution for 6x^2+27x+15=-2x^2-3x-13 equation:

6x^2+27x+15=-2x^2-3x-13

We move all terms to the left:

6x^2+27x+15-(-2x^2-3x-13)=0

We get rid of parentheses

6x^2+2x^2+3x+27x+13+15=0

We add all the numbers together, and all the variables

8x^2+30x+28=0

a = 8; b = 30; c = +28;
Δ = b2-4ac
Δ = 302-4·8·28
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2}{2*8}=\frac{-28}{16}
=-1+3/4
$