3x-7/x+5=x-3/x+2

Solution for 3x-7/x+5=x-3/x+2 equation:

3x-7/x+5=x-3/x+2

We move all terms to the left:

3x-7/x+5-(x-3/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

3x-7/x-x+3/x-2+5=0

We multiply all the terms by the denominator


3x*x-x*x-2*x+5*x-7+3=0

We add all the numbers together, and all the variables

3x+3x*x-x*x-4=0

Wy multiply elements

3x^2-1x^2+3x-4=0

We add all the numbers together, and all the variables

2x^2+3x-4=0

a = 2; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·2·(-4)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*2}=\frac{-3-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*2}=\frac{-3+\sqrt{41}}{4}
$