5/4x-1=5x-1

Solution for 5/4x-1=5x-1 equation:

5/4x-1=5x-1

We move all terms to the left:

5/4x-1-(5x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

5/4x-5x+1-1=0

We multiply all the terms by the denominator


-5x*4x+1*4x-1*4x+5=0

Wy multiply elements

-20x^2+4x-4x+5=0

We add all the numbers together, and all the variables

-20x^2+5=0

a = -20; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-20)·5
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-20}=\frac{-20}{-40}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-20}=\frac{20}{-40}
=-1/2
$