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

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

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

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 3k-10)!=0

k∈R


We get rid of parentheses

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

We calculate fractions


3k/6k^2+(-2k)/6k^2+10+3=0

We add all the numbers together, and all the variables

3k/6k^2+(-2k)/6k^2+13=0

We multiply all the terms by the denominator


3k+(-2k)+13*6k^2=0

Wy multiply elements

78k^2+3k+(-2k)=0

We get rid of parentheses

78k^2+3k-2k=0

We add all the numbers together, and all the variables

78k^2+k=0

a = 78; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·78·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*78}=\frac{-2}{156}
=-1/78
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*78}=\frac{0}{156}
=0
$