2/3k+1/2k=22

Solution for 2/3k+1/2k=22 equation:

2/3k+1/2k=22

We move all terms to the left:

2/3k+1/2k-(22)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We calculate fractions


4k/6k^2+3k/6k^2-22=0

We multiply all the terms by the denominator


4k+3k-22*6k^2=0

We add all the numbers together, and all the variables

7k-22*6k^2=0

Wy multiply elements

-132k^2+7k=0

a = -132; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-132)·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*-132}=\frac{-14}{-264}
=7/132
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-132}=\frac{0}{-264}
=0
$