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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-54x^2)/150x^2+75x/150x^2+(250x+2)/150x^2=0

We multiply all the terms by the denominator


(-54x^2)+75x+(250x+2)=0

We get rid of parentheses

-54x^2+75x+250x+2=0

We add all the numbers together, and all the variables

-54x^2+325x+2=0

a = -54; b = 325; c = +2;
Δ = b2-4ac
Δ = 3252-4·(-54)·2
Δ = 106057
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{-(325)-\sqrt{106057}}{2*-54}=\frac{-325-\sqrt{106057}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(325)+\sqrt{106057}}{2*-54}=\frac{-325+\sqrt{106057}}{-108}
$