1/2k-5=-1/3k

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

1/2k-5=-1/3k

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We get rid of parentheses

1/2k+1/3k-5=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5k-5*6k^2=0

Wy multiply elements

-30k^2+5k=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-30}=\frac{-10}{-60}
=1/6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$