1/6x+37=61-1/3x

Solution for 1/6x+37=61-1/3x equation:

1/6x+37=61-1/3x

We move all terms to the left:

1/6x+37-(61-1/3x)=0


Domain of the equation: 6x!=0

x!=0/6

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

1/6x-(-1/3x+61)+37=0

We get rid of parentheses

1/6x+1/3x-61+37=0

We calculate fractions


3x/18x^2+6x/18x^2-61+37=0

We add all the numbers together, and all the variables

3x/18x^2+6x/18x^2-24=0

We multiply all the terms by the denominator


3x+6x-24*18x^2=0

We add all the numbers together, and all the variables

9x-24*18x^2=0

Wy multiply elements

-432x^2+9x=0

a = -432; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-432)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-432}=\frac{-18}{-864}
=1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-432}=\frac{0}{-864}
=0
$