6k-2k^2=3-k

Solution for 6k-2k^2=3-k equation:

6k-2k^2=3-k

We move all terms to the left:

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

We add all the numbers together, and all the variables

-2k^2+6k-(-1k+3)=0

We get rid of parentheses

-2k^2+6k+1k-3=0

We add all the numbers together, and all the variables

-2k^2+7k-3=0

a = -2; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-2)·(-3)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*-2}=\frac{-12}{-4}
=+3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*-2}=\frac{-2}{-4}
=1/2
$