1/3k+4-2k=-9k

Solution for 1/3k+4-2k=-9k equation:

1/3k+4-2k=-9k

We move all terms to the left:

1/3k+4-2k-(-9k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

-2k+1/3k-(-9k)+4=0

We get rid of parentheses

-2k+1/3k+9k+4=0

We multiply all the terms by the denominator


-2k*3k+9k*3k+4*3k+1=0

Wy multiply elements

-6k^2+27k^2+12k+1=0

We add all the numbers together, and all the variables

21k^2+12k+1=0

a = 21; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·21·1
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{15}}{2*21}=\frac{-12-2\sqrt{15}}{42}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{15}}{2*21}=\frac{-12+2\sqrt{15}}{42}
$