8-3(k+2)k=2-3k

Solution for 8-3(k+2)k=2-3k equation:

8-3(k+2)k=2-3k

We move all terms to the left:

8-3(k+2)k-(2-3k)=0

We add all the numbers together, and all the variables

-3(k+2)k-(-3k+2)+8=0

We multiply parentheses

-3k^2-6k-(-3k+2)+8=0

We get rid of parentheses

-3k^2-6k+3k-2+8=0

We add all the numbers together, and all the variables

-3k^2-3k+6=0

a = -3; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-3)·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*-3}=\frac{-6}{-6}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-3}=\frac{12}{-6}
=-2
$