1/7k-1/14k=-3

Solution for 1/7k-1/14k=-3 equation:

1/7k-1/14k=-3

We move all terms to the left:

1/7k-1/14k-(-3)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 14k!=0

k!=0/14

k!=0

k∈R


We add all the numbers together, and all the variables

1/7k-1/14k+3=0

We calculate fractions


14k/98k^2+(-7k)/98k^2+3=0

We multiply all the terms by the denominator


14k+(-7k)+3*98k^2=0

Wy multiply elements

294k^2+14k+(-7k)=0

We get rid of parentheses

294k^2+14k-7k=0

We add all the numbers together, and all the variables

294k^2+7k=0

a = 294; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·294·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*294}=\frac{-14}{588}
=-1/42
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*294}=\frac{0}{588}
=0
$