3x=2+3/4x-1

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

3x=2+3/4x-1

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-3/4x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-4x-3=0

a = 12; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·12·(-3)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*12}=\frac{4-4\sqrt{10}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*12}=\frac{4+4\sqrt{10}}{24}
$