2/3k-11=4+k

Solution for 2/3k-11=4+k equation:

2/3k-11=4+k

We move all terms to the left:

2/3k-11-(4+k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

2/3k-(k+4)-11=0

We get rid of parentheses

2/3k-k-4-11=0

We multiply all the terms by the denominator


-k*3k-4*3k-11*3k+2=0

Wy multiply elements

-3k^2-12k-33k+2=0

We add all the numbers together, and all the variables

-3k^2-45k+2=0

a = -3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·(-3)·2
Δ = 2049
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{-(-45)-\sqrt{2049}}{2*-3}=\frac{45-\sqrt{2049}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*-3}=\frac{45+\sqrt{2049}}{-6}
$