x-1=11x-1/x-5

Solution for x-1=11x-1/x-5 equation:

x-1=11x-1/x-5

We move all terms to the left:

x-1-(11x-1/x-5)=0


Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

x-11x+1/x+5-1=0

We multiply all the terms by the denominator


x*x-11x*x+5*x-1*x+1=0

We add all the numbers together, and all the variables

4x+x*x-11x*x+1=0

Wy multiply elements

x^2-11x^2+4x+1=0

We add all the numbers together, and all the variables

-10x^2+4x+1=0

a = -10; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-10)·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*-10}=\frac{-4-2\sqrt{14}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*-10}=\frac{-4+2\sqrt{14}}{-20}
$