1/3x+5=1/2x+6

Solution for 1/3x+5=1/2x+6 equation:

1/3x+5=1/2x+6

We move all terms to the left:

1/3x+5-(1/2x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

1/3x-1/2x-6+5=0

We calculate fractions


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

We add all the numbers together, and all the variables

2x/6x^2+(-3x)/6x^2-1=0

We multiply all the terms by the denominator


2x+(-3x)-1*6x^2=0

Wy multiply elements

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

We get rid of parentheses

-6x^2+2x-3x=0

We add all the numbers together, and all the variables

-6x^2-1x=0

a = -6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-6)·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*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-6}=\frac{2}{-12}
=-1/6
$