2/5k-1/k+12=8

Solution for 2/5k-1/k+12=8 equation:

2/5k-1/k+12=8

We move all terms to the left:

2/5k-1/k+12-(8)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

2/5k-1/k+4=0

We calculate fractions


2k/5k^2+(-5k)/5k^2+4=0

We multiply all the terms by the denominator


2k+(-5k)+4*5k^2=0

Wy multiply elements

20k^2+2k+(-5k)=0

We get rid of parentheses

20k^2+2k-5k=0

We add all the numbers together, and all the variables

20k^2-3k=0

a = 20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·20·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*20}=\frac{0}{40}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*20}=\frac{6}{40}
=3/20
$