3/8k-9=1/5k+3

Solution for 3/8k-9=1/5k+3 equation:

3/8k-9=1/5k+3

We move all terms to the left:

3/8k-9-(1/5k+3)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 5k+3)!=0

k∈R


We get rid of parentheses

3/8k-1/5k-3-9=0

We calculate fractions


15k/40k^2+(-8k)/40k^2-3-9=0

We add all the numbers together, and all the variables

15k/40k^2+(-8k)/40k^2-12=0

We multiply all the terms by the denominator


15k+(-8k)-12*40k^2=0

Wy multiply elements

-480k^2+15k+(-8k)=0

We get rid of parentheses

-480k^2+15k-8k=0

We add all the numbers together, and all the variables

-480k^2+7k=0

a = -480; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-480)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-480}=\frac{-14}{-960}
=7/480
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-480}=\frac{0}{-960}
=0
$