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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/48x^2+16x/48x^2+(-12x)/48x^2-3=0

Fractions to decimals

16x/48x^2+(-12x)/48x^2-3+1=0

We multiply all the terms by the denominator


16x+(-12x)-3*48x^2+1*48x^2=0

Wy multiply elements

-144x^2+48x^2+16x+(-12x)=0

We get rid of parentheses

-144x^2+48x^2+16x-12x=0

We add all the numbers together, and all the variables

-96x^2+4x=0

a = -96; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-96)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-96}=\frac{-8}{-192}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-96}=\frac{0}{-192}
=0
$