2x^2+5x+6=-2x^2-x+30

Solution for 2x^2+5x+6=-2x^2-x+30 equation:

2x^2+5x+6=-2x^2-x+30

We move all terms to the left:

2x^2+5x+6-(-2x^2-x+30)=0

We get rid of parentheses

2x^2+2x^2+x+5x-30+6=0

We add all the numbers together, and all the variables

4x^2+6x-24=0

a = 4; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·4·(-24)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*4}=\frac{-6-2\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*4}=\frac{-6+2\sqrt{105}}{8}
$