2x-1=3/4x-1

Solution for 2x-1=3/4x-1 equation:

2x-1=3/4x-1

We move all terms to the left:

2x-1-(3/4x-1)=0


Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

2x-3/4x+1-1=0

We multiply all the terms by the denominator


2x*4x+1*4x-1*4x-3=0

Wy multiply elements

8x^2+4x-4x-3=0

We add all the numbers together, and all the variables

8x^2-3=0

a = 8; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·8·(-3)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*8}=\frac{0-4\sqrt{6}}{16}
=-\frac{4\sqrt{6}}{16}
=-\frac{\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*8}=\frac{0+4\sqrt{6}}{16}
=\frac{4\sqrt{6}}{16}
=\frac{\sqrt{6}}{4}
$