5x-7/x-1=x+1

Solution for 5x-7/x-1=x+1 equation:

5x-7/x-1=x+1

We move all terms to the left:

5x-7/x-1-(x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5x-7/x-x-1-1=0

We multiply all the terms by the denominator


5x*x-x*x-1*x-1*x-7=0

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-1x^2-2x-7=0

We add all the numbers together, and all the variables

4x^2-2x-7=0

a = 4; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·4·(-7)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*4}=\frac{2-2\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*4}=\frac{2+2\sqrt{29}}{8}
$