5/3x-7=4+1/6x

Solution for 5/3x-7=4+1/6x equation:

5/3x-7=4+1/6x

We move all terms to the left:

5/3x-7-(4+1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(1/6x+4)-7=0

We get rid of parentheses

5/3x-1/6x-4-7=0

We calculate fractions


30x/18x^2+(-3x)/18x^2-4-7=0

We add all the numbers together, and all the variables

30x/18x^2+(-3x)/18x^2-11=0

We multiply all the terms by the denominator


30x+(-3x)-11*18x^2=0

Wy multiply elements

-198x^2+30x+(-3x)=0

We get rid of parentheses

-198x^2+30x-3x=0

We add all the numbers together, and all the variables

-198x^2+27x=0

a = -198; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-198)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-198}=\frac{-54}{-396}
=3/22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-198}=\frac{0}{-396}
=0
$