2/3k+1/5k=2

Solution for 2/3k+1/5k=2 equation:

2/3k+1/5k=2

We move all terms to the left:

2/3k+1/5k-(2)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We calculate fractions


10k/15k^2+3k/15k^2-2=0

We multiply all the terms by the denominator


10k+3k-2*15k^2=0

We add all the numbers together, and all the variables

13k-2*15k^2=0

Wy multiply elements

-30k^2+13k=0

a = -30; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-30)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-30}=\frac{-26}{-60}
=13/30
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-30}=\frac{0}{-60}
=0
$