2x+3/x+4=x/x-2

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

2x+3/x+4=x/x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

2x+3/x-x/x+2+4=0

Fractions to decimals

3/x+2x+2+4+1=0

We multiply all the terms by the denominator


2x*x+2*x+4*x+1*x+3=0

We add all the numbers together, and all the variables

7x+2x*x+3=0

Wy multiply elements

2x^2+7x+3=0

a = 2; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·2·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*2}=\frac{-2}{4}
=-1/2
$