1/3k+6/8k=-12

Solution for 1/3k+6/8k=-12 equation:

1/3k+6/8k=-12

We move all terms to the left:

1/3k+6/8k-(-12)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We add all the numbers together, and all the variables

1/3k+6/8k+12=0

We calculate fractions


8k/24k^2+18k/24k^2+12=0

We multiply all the terms by the denominator


8k+18k+12*24k^2=0

We add all the numbers together, and all the variables

26k+12*24k^2=0

Wy multiply elements

288k^2+26k=0

a = 288; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·288·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*288}=\frac{-52}{576}
=-13/144
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*288}=\frac{0}{576}
=0
$