2x-11=1/2x-1

Solution for 2x-11=1/2x-1 equation:

2x-11=1/2x-1

We move all terms to the left:

2x-11-(1/2x-1)=0


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

2x-1/2x+1-11=0

We multiply all the terms by the denominator


2x*2x+1*2x-11*2x-1=0

Wy multiply elements

4x^2+2x-22x-1=0

We add all the numbers together, and all the variables

4x^2-20x-1=0

a = 4; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·4·(-1)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*4}=\frac{20-4\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*4}=\frac{20+4\sqrt{26}}{8}
$