1/5k-3=3/10k

Solution for 1/5k-3=3/10k equation:

1/5k-3=3/10k

We move all terms to the left:

1/5k-3-(3/10k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 10k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

1/5k-(+3/10k)-3=0

We get rid of parentheses

1/5k-3/10k-3=0

We calculate fractions


10k/50k^2+(-15k)/50k^2-3=0

We multiply all the terms by the denominator


10k+(-15k)-3*50k^2=0

Wy multiply elements

-150k^2+10k+(-15k)=0

We get rid of parentheses

-150k^2+10k-15k=0

We add all the numbers together, and all the variables

-150k^2-5k=0

a = -150; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-150)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-150}=\frac{0}{-300}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-150}=\frac{10}{-300}
=-1/30
$