2(x+4)/x-2+3=2x+1/x-2

Solution for 2(x+4)/x-2+3=2x+1/x-2 equation:

2(x+4)/x-2+3=2x+1/x-2

We move all terms to the left:

2(x+4)/x-2+3-(2x+1/x-2)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

2(x+4)/x-(2x+1/x-2)+1=0

We get rid of parentheses

2(x+4)/x-2x-1/x+2+1=0

We multiply all the terms by the denominator


2(x+4)-2x*x+2*x+1*x-1=0

We add all the numbers together, and all the variables

3x+2(x+4)-2x*x-1=0

We multiply parentheses

3x+2x-2x*x+8-1=0

Wy multiply elements

-2x^2+3x+2x+8-1=0

We add all the numbers together, and all the variables

-2x^2+5x+7=0

a = -2; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-2}=\frac{4}{-4}
=-1
$