2x-1=3/4x+x

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

2x-1=3/4x+x

We move all terms to the left:

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


Domain of the equation: 4x+x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-4x-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$