5x-5/x+1=3

Solution for 5x-5/x+1=3 equation:

5x-5/x+1=3

We move all terms to the left:

5x-5/x+1-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-5/x-2=0

We multiply all the terms by the denominator


5x*x-2*x-5=0

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-2x-5=0

a = 5; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·5·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{26}}{2*5}=\frac{2-2\sqrt{26}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{26}}{2*5}=\frac{2+2\sqrt{26}}{10}
$