6/x+16=7/3x+3

Solution for 6/x+16=7/3x+3 equation:

6/x+16=7/3x+3

We move all terms to the left:

6/x+16-(7/3x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

6/x-7/3x-3+16=0

We calculate fractions


18x/3x^2+(-7x)/3x^2-3+16=0

We add all the numbers together, and all the variables

18x/3x^2+(-7x)/3x^2+13=0

We multiply all the terms by the denominator


18x+(-7x)+13*3x^2=0

Wy multiply elements

39x^2+18x+(-7x)=0

We get rid of parentheses

39x^2+18x-7x=0

We add all the numbers together, and all the variables

39x^2+11x=0

a = 39; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·39·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*39}=\frac{-22}{78}
=-11/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*39}=\frac{0}{78}
=0
$