1/3x+1/4=3/5x

Solution for 1/3x+1/4=3/5x equation:

1/3x+1/4=3/5x

We move all terms to the left:

1/3x+1/4-(3/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+3/5x)+1/4=0

We get rid of parentheses

1/3x-3/5x+1/4=0

We calculate fractions


75x^2/240x^2+80x/240x^2+(-144x)/240x^2=0

We multiply all the terms by the denominator


75x^2+80x+(-144x)=0

We get rid of parentheses

75x^2+80x-144x=0

We add all the numbers together, and all the variables

75x^2-64x=0

a = 75; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·75·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*75}=\frac{0}{150}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*75}=\frac{128}{150}
=64/75
$