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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9x/12x^2+(-8x)/12x^2-1-3=0

We add all the numbers together, and all the variables

9x/12x^2+(-8x)/12x^2-4=0

We multiply all the terms by the denominator


9x+(-8x)-4*12x^2=0

Wy multiply elements

-48x^2+9x+(-8x)=0

We get rid of parentheses

-48x^2+9x-8x=0

We add all the numbers together, and all the variables

-48x^2+x=0

a = -48; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-48)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-48}=\frac{-2}{-96}
=1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-48}=\frac{0}{-96}
=0
$