2/5k+4=2/3k

Solution for 2/5k+4=2/3k equation:

2/5k+4=2/3k

We move all terms to the left:

2/5k+4-(2/3k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/5k-(+2/3k)+4=0

We get rid of parentheses

2/5k-2/3k+4=0

We calculate fractions


6k/15k^2+(-10k)/15k^2+4=0

We multiply all the terms by the denominator


6k+(-10k)+4*15k^2=0

Wy multiply elements

60k^2+6k+(-10k)=0

We get rid of parentheses

60k^2+6k-10k=0

We add all the numbers together, and all the variables

60k^2-4k=0

a = 60; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·60·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*60}=\frac{0}{120}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*60}=\frac{8}{120}
=1/15
$