1/5k-1/6=4/3k

Solution for 1/5k-1/6=4/3k equation:

1/5k-1/6=4/3k

We move all terms to the left:

1/5k-1/6-(4/3k)=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

1/5k-(+4/3k)-1/6=0

We get rid of parentheses

1/5k-4/3k-1/6=0

We calculate fractions


(-45k^2)/540k^2+108k/540k^2+(-720k)/540k^2=0

We multiply all the terms by the denominator


(-45k^2)+108k+(-720k)=0

We get rid of parentheses

-45k^2+108k-720k=0

We add all the numbers together, and all the variables

-45k^2-612k=0

a = -45; b = -612; c = 0;
Δ = b2-4ac
Δ = -6122-4·(-45)·0
Δ = 374544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{374544}=612$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-612)-612}{2*-45}=\frac{0}{-90}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-612)+612}{2*-45}=\frac{1224}{-90}
=-13+3/5
$