1/3k+80=1/2k=120

Solution for 1/3k+80=1/2k=120 equation:

1/3k+80=1/2k=120

We move all terms to the left:

1/3k+80-(1/2k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

1/3k-(+1/2k)+80=0

We get rid of parentheses

1/3k-1/2k+80=0

We calculate fractions


2k/6k^2+(-3k)/6k^2+80=0

We multiply all the terms by the denominator


2k+(-3k)+80*6k^2=0

Wy multiply elements

480k^2+2k+(-3k)=0

We get rid of parentheses

480k^2+2k-3k=0

We add all the numbers together, and all the variables

480k^2-1k=0

a = 480; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·480·0
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*480}=\frac{0}{960}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*480}=\frac{2}{960}
=1/480
$