2x+7/x-7=3x+8/x-2

Solution for 2x+7/x-7=3x+8/x-2 equation:

2x+7/x-7=3x+8/x-2

We move all terms to the left:

2x+7/x-7-(3x+8/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+7/x-3x-8/x+2-7=0

We multiply all the terms by the denominator


2x*x-3x*x+2*x-7*x+7-8=0

We add all the numbers together, and all the variables

-5x+2x*x-3x*x-1=0

Wy multiply elements

2x^2-3x^2-5x-1=0

We add all the numbers together, and all the variables

-1x^2-5x-1=0

a = -1; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-1)·(-1)
Δ = 21
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{-(-5)-\sqrt{21}}{2*-1}=\frac{5-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{21}}{2*-1}=\frac{5+\sqrt{21}}{-2}
$