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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


36x^2/48x^2+36x/48x^2+(-16x)/48x^2-3=0

We multiply all the terms by the denominator


36x^2+36x+(-16x)-3*48x^2=0

Wy multiply elements

36x^2-144x^2+36x+(-16x)=0

We get rid of parentheses

36x^2-144x^2+36x-16x=0

We add all the numbers together, and all the variables

-108x^2+20x=0

a = -108; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-108)·0
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{-(20)-20}{2*-108}=\frac{-40}{-216}
=5/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-108}=\frac{0}{-216}
=0
$