1/4k+6=-3/12k+3

Solution for 1/4k+6=-3/12k+3 equation:

1/4k+6=-3/12k+3

We move all terms to the left:

1/4k+6-(-3/12k+3)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 12k+3)!=0

k∈R


We get rid of parentheses

1/4k+3/12k-3+6=0

We calculate fractions


12k/48k^2+12k/48k^2-3+6=0

We add all the numbers together, and all the variables

12k/48k^2+12k/48k^2+3=0

We multiply all the terms by the denominator


12k+12k+3*48k^2=0

We add all the numbers together, and all the variables

24k+3*48k^2=0

Wy multiply elements

144k^2+24k=0

a = 144; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·144·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*144}=\frac{-48}{288}
=-1/6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*144}=\frac{0}{288}
=0
$