12+k=-9-1/3k

Solution for 12+k=-9-1/3k equation:

12+k=-9-1/3k

We move all terms to the left:

12+k-(-9-1/3k)=0


Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

k-(-1/3k-9)+12=0

We get rid of parentheses

k+1/3k+9+12=0

We multiply all the terms by the denominator


k*3k+9*3k+12*3k+1=0

Wy multiply elements

3k^2+27k+36k+1=0

We add all the numbers together, and all the variables

3k^2+63k+1=0

a = 3; b = 63; c = +1;
Δ = b2-4ac
Δ = 632-4·3·1
Δ = 3957
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-\sqrt{3957}}{2*3}=\frac{-63-\sqrt{3957}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{3957}}{2*3}=\frac{-63+\sqrt{3957}}{6}
$