2/3k+1/4k=20

Solution for 2/3k+1/4k=20 equation:

2/3k+1/4k=20

We move all terms to the left:

2/3k+1/4k-(20)=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


8k/12k^2+3k/12k^2-20=0

We multiply all the terms by the denominator


8k+3k-20*12k^2=0

We add all the numbers together, and all the variables

11k-20*12k^2=0

Wy multiply elements

-240k^2+11k=0

a = -240; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-240)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-240}=\frac{-22}{-480}
=11/240
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-240}=\frac{0}{-480}
=0
$