2/(x+2)=2x-8

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

2/(x+2)=2x-8

We move all terms to the left:

2/(x+2)-(2x-8)=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∈R


We get rid of parentheses

2/(x+2)-2x+8=0

We multiply all the terms by the denominator


-2x*(x+2)+8*(x+2)+2=0

We multiply parentheses

-2x^2-4x+8x+16+2=0

We add all the numbers together, and all the variables

-2x^2+4x+18=0

a = -2; b = 4; c = +18;
Δ = b2-4ac
Δ = 42-4·(-2)·18
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*-2}=\frac{-4-4\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*-2}=\frac{-4+4\sqrt{10}}{-4}
$