5x-7/x+1=2

Solution for 5x-7/x+1=2 equation:

5x-7/x+1=2

We move all terms to the left:

5x-7/x+1-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-7/x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-1x-7=0

a = 5; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·5·(-7)
Δ = 141
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{-(-1)-\sqrt{141}}{2*5}=\frac{1-\sqrt{141}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{141}}{2*5}=\frac{1+\sqrt{141}}{10}
$