1/3k+1/4k=1

Solution for 1/3k+1/4k=1 equation:

1/3k+1/4k=1

We move all terms to the left:

1/3k+1/4k-(1)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We calculate fractions


4k/12k^2+3k/12k^2-1=0

We multiply all the terms by the denominator


4k+3k-1*12k^2=0

We add all the numbers together, and all the variables

7k-1*12k^2=0

Wy multiply elements

-12k^2+7k=0

a = -12; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-12)·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*-12}=\frac{-14}{-24}
=7/12
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-12}=\frac{0}{-24}
=0
$