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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/6x^2+(-9x)/6x^2-3+4=0

We add all the numbers together, and all the variables

2x/6x^2+(-9x)/6x^2+1=0

We multiply all the terms by the denominator


2x+(-9x)+1*6x^2=0

Wy multiply elements

6x^2+2x+(-9x)=0

We get rid of parentheses

6x^2+2x-9x=0

We add all the numbers together, and all the variables

6x^2-7x=0

a = 6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*6}=\frac{14}{12}
=1+1/6
$