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

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

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

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k+3)!=0

k∈R


We get rid of parentheses

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

We calculate fractions


6k/15k^2+(-25k)/15k^2-3-2=0

We add all the numbers together, and all the variables

6k/15k^2+(-25k)/15k^2-5=0

We multiply all the terms by the denominator


6k+(-25k)-5*15k^2=0

Wy multiply elements

-75k^2+6k+(-25k)=0

We get rid of parentheses

-75k^2+6k-25k=0

We add all the numbers together, and all the variables

-75k^2-19k=0

a = -75; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-75)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-75}=\frac{0}{-150}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-75}=\frac{38}{-150}
=-19/75
$