3x-1/x-5=2

Solution for 3x-1/x-5=2 equation:

3x-1/x-5=2

We move all terms to the left:

3x-1/x-5-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-1/x-7=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-7x-1=0

a = 3; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·3·(-1)
Δ = 61
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{61}}{2*3}=\frac{7-\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*3}=\frac{7+\sqrt{61}}{6}
$