1/3k+2=1/6k-3

Solution for 1/3k+2=1/6k-3 equation:

1/3k+2=1/6k-3

We move all terms to the left:

1/3k+2-(1/6k-3)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 6k-3)!=0

k∈R


We get rid of parentheses

1/3k-1/6k+3+2=0

We calculate fractions


6k/18k^2+(-3k)/18k^2+3+2=0

We add all the numbers together, and all the variables

6k/18k^2+(-3k)/18k^2+5=0

We multiply all the terms by the denominator


6k+(-3k)+5*18k^2=0

Wy multiply elements

90k^2+6k+(-3k)=0

We get rid of parentheses

90k^2+6k-3k=0

We add all the numbers together, and all the variables

90k^2+3k=0

a = 90; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·90·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*90}=\frac{-6}{180}
=-1/30
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*90}=\frac{0}{180}
=0
$