5/2x-1=x-1

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

5/2x-1=x-1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-x+1-1=0

We multiply all the terms by the denominator


-x*2x+1*2x-1*2x+5=0

Wy multiply elements

-2x^2+2x-2x+5=0

We add all the numbers together, and all the variables

-2x^2+5=0

a = -2; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-2)·5
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-2}=\frac{0-2\sqrt{10}}{-4}
=-\frac{2\sqrt{10}}{-4}
=-\frac{\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-2}=\frac{0+2\sqrt{10}}{-4}
=\frac{2\sqrt{10}}{-4}
=\frac{\sqrt{10}}{-2}
$