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

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

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

We move all terms to the left:

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


Domain of the equation: 3x+5)!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x/6x^2+(-3x)/6x^2+5=0

We multiply all the terms by the denominator


2x+(-3x)+5*6x^2=0

Wy multiply elements

30x^2+2x+(-3x)=0

We get rid of parentheses

30x^2+2x-3x=0

We add all the numbers together, and all the variables

30x^2-1x=0

a = 30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·30·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*30}=\frac{2}{60}
=1/30
$