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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*3x-1*3x+5-5=0

We add all the numbers together, and all the variables

x*3x-1*3x=0

Wy multiply elements

3x^2-3x=0

a = 3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·3·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*3}=\frac{6}{6}
=1
$