3/5k-1/10=1/2k+1

Solution for 3/5k-1/10=1/2k+1 equation:

3/5k-1/10=1/2k+1

We move all terms to the left:

3/5k-1/10-(1/2k+1)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 2k+1)!=0

k∈R


We get rid of parentheses

3/5k-1/2k-1-1/10=0

We calculate fractions


(-20k^2)/100k^2+60k/100k^2+(-50k)/100k^2-1=0

We multiply all the terms by the denominator


(-20k^2)+60k+(-50k)-1*100k^2=0

Wy multiply elements

(-20k^2)-100k^2+60k+(-50k)=0

We get rid of parentheses

-20k^2-100k^2+60k-50k=0

We add all the numbers together, and all the variables

-120k^2+10k=0

a = -120; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-120)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-120}=\frac{-20}{-240}
=1/12
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-120}=\frac{0}{-240}
=0
$