2/7k=-3+1/14k

Solution for 2/7k=-3+1/14k equation:

2/7k=-3+1/14k

We move all terms to the left:

2/7k-(-3+1/14k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 14k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/7k-(1/14k-3)=0

We get rid of parentheses

2/7k-1/14k+3=0

We calculate fractions


28k/98k^2+(-7k)/98k^2+3=0

We multiply all the terms by the denominator


28k+(-7k)+3*98k^2=0

Wy multiply elements

294k^2+28k+(-7k)=0

We get rid of parentheses

294k^2+28k-7k=0

We add all the numbers together, and all the variables

294k^2+21k=0

a = 294; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·294·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*294}=\frac{-42}{588}
=-1/14
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*294}=\frac{0}{588}
=0
$