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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3x+(-8x)+2*12x^2=0

Wy multiply elements

24x^2+3x+(-8x)=0

We get rid of parentheses

24x^2+3x-8x=0

We add all the numbers together, and all the variables

24x^2-5x=0

a = 24; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·24·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*24}=\frac{10}{48}
=5/24
$