3/k+1=6/5k-1

Solution for 3/k+1=6/5k-1 equation:

3/k+1=6/5k-1

We move all terms to the left:

3/k+1-(6/5k-1)=0


Domain of the equation: k!=0

k∈R



Domain of the equation: 5k-1)!=0

k∈R


We get rid of parentheses

3/k-6/5k+1+1=0

We calculate fractions


15k/5k^2+(-6k)/5k^2+1+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

10k^2+15k-6k=0

We add all the numbers together, and all the variables

10k^2+9k=0

a = 10; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·10·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*10}=\frac{-18}{20}
=-9/10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*10}=\frac{0}{20}
=0
$