2k^2=6-k

Solution for 2k^2=6-k equation:

2k^2=6-k

We move all terms to the left:

2k^2-(6-k)=0

We add all the numbers together, and all the variables

2k^2-(-1k+6)=0

We get rid of parentheses

2k^2+1k-6=0

We add all the numbers together, and all the variables

2k^2+k-6=0

a = 2; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·2·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*2}=\frac{-8}{4}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*2}=\frac{6}{4}
=1+1/2
$