3/4k+38/k=12

Solution for 3/4k+38/k=12 equation:

3/4k+38/k=12

We move all terms to the left:

3/4k+38/k-(12)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: k!=0

k∈R


We calculate fractions


3k/4k^2+152k/4k^2-12=0

We multiply all the terms by the denominator


3k+152k-12*4k^2=0

We add all the numbers together, and all the variables

155k-12*4k^2=0

Wy multiply elements

-48k^2+155k=0

a = -48; b = 155; c = 0;
Δ = b2-4ac
Δ = 1552-4·(-48)·0
Δ = 24025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24025}=155$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(155)-155}{2*-48}=\frac{-310}{-96}
=3+11/48
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(155)+155}{2*-48}=\frac{0}{-96}
=0
$