2/6k+80=1/2k+120

Solution for 2/6k+80=1/2k+120 equation:

2/6k+80=1/2k+120

We move all terms to the left:

2/6k+80-(1/2k+120)=0


Domain of the equation: 6k!=0

k!=0/6

k!=0

k∈R



Domain of the equation: 2k+120)!=0

k∈R


We get rid of parentheses

2/6k-1/2k-120+80=0

We calculate fractions


4k/12k^2+(-6k)/12k^2-120+80=0

We add all the numbers together, and all the variables

4k/12k^2+(-6k)/12k^2-40=0

We multiply all the terms by the denominator


4k+(-6k)-40*12k^2=0

Wy multiply elements

-480k^2+4k+(-6k)=0

We get rid of parentheses

-480k^2+4k-6k=0

We add all the numbers together, and all the variables

-480k^2-2k=0

a = -480; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-480)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-480}=\frac{0}{-960}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-480}=\frac{4}{-960}
=-1/240
$