(3x^2+10x+8x)/(-x-2)=-2

Solution for (3x^2+10x+8x)/(-x-2)=-2 equation:

(3x^2+10x+8x)/(-x-2)=-2

We move all terms to the left:

(3x^2+10x+8x)/(-x-2)-(-2)=0


Domain of the equation: (-x-2)!=0

We move all terms containing x to the left, all other terms to the right

-x!=2

x!=2/-1

x!=-2

x∈R


We add all the numbers together, and all the variables

(3x^2+10x+8x)/(-1x-2)-(-2)=0

We add all the numbers together, and all the variables

(3x^2+10x+8x)/(-1x-2)+2=0

We multiply all the terms by the denominator


(3x^2+10x+8x)+2*(-1x-2)=0

We multiply parentheses

(3x^2+10x+8x)-2x-4=0

We get rid of parentheses

3x^2+10x+8x-2x-4=0

We add all the numbers together, and all the variables

3x^2+16x-4=0

a = 3; b = 16; c = -4;
Δ = b2-4ac
Δ = 162-4·3·(-4)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{19}}{2*3}=\frac{-16-4\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{19}}{2*3}=\frac{-16+4\sqrt{19}}{6}
$