1/x+2/3x=5

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

1/x+2/3x=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


3x+2x-5*3x^2=0

We add all the numbers together, and all the variables

5x-5*3x^2=0

Wy multiply elements

-15x^2+5x=0

a = -15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-15)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-15}=\frac{-10}{-30}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-15}=\frac{0}{-30}
=0
$