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-3=0

We multiply all the terms by the denominator


5x*x-3*x-7=0

We add all the numbers together, and all the variables

-3x+5x*x-7=0

Wy multiply elements

5x^2-3x-7=0

a = 5; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·5·(-7)
Δ = 149
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{-(-3)-\sqrt{149}}{2*5}=\frac{3-\sqrt{149}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{149}}{2*5}=\frac{3+\sqrt{149}}{10}
$