5x-1/x-1=0

Solution for 5x-1/x-1=0 equation:

5x-1/x-1=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-1x-1=0

a = 5; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·5·(-1)
Δ = 21
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{21}}{2*5}=\frac{1-\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*5}=\frac{1+\sqrt{21}}{10}
$