1/3k-1/2k=5

Solution for 1/3k-1/2k=5 equation:

1/3k-1/2k=5

We move all terms to the left:

1/3k-1/2k-(5)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-30k^2+2k+(-3k)=0

We get rid of parentheses

-30k^2+2k-3k=0

We add all the numbers together, and all the variables

-30k^2-1k=0

a = -30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-30}=\frac{0}{-60}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-30}=\frac{2}{-60}
=-1/30
$