5/3x+13=1/6x+17

Solution for 5/3x+13=1/6x+17 equation:

5/3x+13=1/6x+17

We move all terms to the left:

5/3x+13-(1/6x+17)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+17)!=0

x∈R


We get rid of parentheses

5/3x-1/6x-17+13=0

We calculate fractions


30x/18x^2+(-3x)/18x^2-17+13=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-72x^2+30x+(-3x)=0

We get rid of parentheses

-72x^2+30x-3x=0

We add all the numbers together, and all the variables

-72x^2+27x=0

a = -72; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-72)·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*-72}=\frac{-54}{-144}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-72}=\frac{0}{-144}
=0
$