2/4k-1/14k=-3

Solution for 2/4k-1/14k=-3 equation:

2/4k-1/14k=-3

We move all terms to the left:

2/4k-1/14k-(-3)=0


Domain of the equation: 4k!=0

k!=0/4

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

2/4k-1/14k+3=0

We calculate fractions


28k/56k^2+(-4k)/56k^2+3=0

We multiply all the terms by the denominator


28k+(-4k)+3*56k^2=0

Wy multiply elements

168k^2+28k+(-4k)=0

We get rid of parentheses

168k^2+28k-4k=0

We add all the numbers together, and all the variables

168k^2+24k=0

a = 168; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·168·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*168}=\frac{-48}{336}
=-1/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*168}=\frac{0}{336}
=0
$