1/6k+1/8k=1

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

1/6k+1/8k=1

We move all terms to the left:

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


Domain of the equation: 6k!=0

k!=0/6

k!=0

k∈R



Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We calculate fractions


8k/48k^2+6k/48k^2-1=0

We multiply all the terms by the denominator


8k+6k-1*48k^2=0

We add all the numbers together, and all the variables

14k-1*48k^2=0

Wy multiply elements

-48k^2+14k=0

a = -48; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-48)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-48}=\frac{-28}{-96}
=7/24
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-48}=\frac{0}{-96}
=0
$