1/6k+1/3k=3/8

Solution for 1/6k+1/3k=3/8 equation:

1/6k+1/3k=3/8

We move all terms to the left:

1/6k+1/3k-(3/8)=0


Domain of the equation: 6k!=0

k!=0/6

k!=0

k∈R



Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

1/6k+1/3k-(+3/8)=0

We get rid of parentheses

1/6k+1/3k-3/8=0

We calculate fractions


(-162k^2)/1152k^2+192k/1152k^2+384k/1152k^2=0

We multiply all the terms by the denominator


(-162k^2)+192k+384k=0

We add all the numbers together, and all the variables

(-162k^2)+576k=0

We get rid of parentheses

-162k^2+576k=0

a = -162; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·(-162)·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*-162}=\frac{-1152}{-324}
=3+5/9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*-162}=\frac{0}{-324}
=0
$