2(x^2+6)+5x=-9x-8

Solution for 2(x^2+6)+5x=-9x-8 equation:

2(x^2+6)+5x=-9x-8

We move all terms to the left:

2(x^2+6)+5x-(-9x-8)=0

We add all the numbers together, and all the variables

5x+2(x^2+6)-(-9x-8)=0

We multiply parentheses

2x^2+5x-(-9x-8)+12=0

We get rid of parentheses

2x^2+5x+9x+8+12=0

We add all the numbers together, and all the variables

2x^2+14x+20=0

a = 2; b = 14; c = +20;
Δ = b2-4ac
Δ = 142-4·2·20
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*2}=\frac{-8}{4}
=-2
$