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

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

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

We move all terms to the left:

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

We calculate fractions


4x/108x^2+(-27x)/108x^2+8x/108x^2-3=0

We multiply all the terms by the denominator


4x+(-27x)+8x-3*108x^2=0

We add all the numbers together, and all the variables

12x+(-27x)-3*108x^2=0

Wy multiply elements

-324x^2+12x+(-27x)=0

We get rid of parentheses

-324x^2+12x-27x=0

We add all the numbers together, and all the variables

-324x^2-15x=0

a = -324; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-324)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-324}=\frac{0}{-648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-324}=\frac{30}{-648}
=-5/108
$