1/4k=3/8k-14

Solution for 1/4k=3/8k-14 equation:

1/4k=3/8k-14

We move all terms to the left:

1/4k-(3/8k-14)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k-14)!=0

k∈R


We get rid of parentheses

1/4k-3/8k+14=0

We calculate fractions


8k/32k^2+(-12k)/32k^2+14=0

We multiply all the terms by the denominator


8k+(-12k)+14*32k^2=0

Wy multiply elements

448k^2+8k+(-12k)=0

We get rid of parentheses

448k^2+8k-12k=0

We add all the numbers together, and all the variables

448k^2-4k=0

a = 448; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·448·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*448}=\frac{0}{896}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*448}=\frac{8}{896}
=1/112
$