1/3k+1/5k=1

Solution for 1/3k+1/5k=1 equation:

1/3k+1/5k=1

We move all terms to the left:

1/3k+1/5k-(1)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We calculate fractions


5k/15k^2+3k/15k^2-1=0

We multiply all the terms by the denominator


5k+3k-1*15k^2=0

We add all the numbers together, and all the variables

8k-1*15k^2=0

Wy multiply elements

-15k^2+8k=0

a = -15; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-15)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-15}=\frac{-16}{-30}
=8/15
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-15}=\frac{0}{-30}
=0
$