1/3x+2/5x=1/3x+4

Solution for 1/3x+2/5x=1/3x+4 equation:

1/3x+2/5x=1/3x+4

We move all terms to the left:

1/3x+2/5x-(1/3x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/3x+2/5x-1/3x-4=0

We calculate fractions


(-5x+1)/15x^2+6x/15x^2-4=0

We multiply all the terms by the denominator


(-5x+1)+6x-4*15x^2=0

We add all the numbers together, and all the variables

6x+(-5x+1)-4*15x^2=0

Wy multiply elements

-60x^2+6x+(-5x+1)=0

We get rid of parentheses

-60x^2+6x-5x+1=0

We add all the numbers together, and all the variables

-60x^2+x+1=0

a = -60; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-60)·1
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{241}}{2*-60}=\frac{-1-\sqrt{241}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*-60}=\frac{-1+\sqrt{241}}{-120}
$