3x-7/x+1=7x/x+1

Solution for 3x-7/x+1=7x/x+1 equation:

3x-7/x+1=7x/x+1

We move all terms to the left:

3x-7/x+1-(7x/x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

3x-7/x-7x/x-1+1=0

We multiply all the terms by the denominator


3x*x-7x-1*x+1*x-7=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-7x-7=0

a = 3; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·3·(-7)
Δ = 133
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{-(-7)-\sqrt{133}}{2*3}=\frac{7-\sqrt{133}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{133}}{2*3}=\frac{7+\sqrt{133}}{6}
$