5/6x-5=31+1/3x

Solution for 5/6x-5=31+1/3x equation:

5/6x-5=31+1/3x

We move all terms to the left:

5/6x-5-(31+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

5/6x-(1/3x+31)-5=0

We get rid of parentheses

5/6x-1/3x-31-5=0

We calculate fractions


15x/18x^2+(-6x)/18x^2-31-5=0

We add all the numbers together, and all the variables

15x/18x^2+(-6x)/18x^2-36=0

We multiply all the terms by the denominator


15x+(-6x)-36*18x^2=0

Wy multiply elements

-648x^2+15x+(-6x)=0

We get rid of parentheses

-648x^2+15x-6x=0

We add all the numbers together, and all the variables

-648x^2+9x=0

a = -648; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-648)·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*-648}=\frac{-18}{-1296}
=1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-648}=\frac{0}{-1296}
=0
$