k^2=64-2k

Solution for k^2=64-2k equation:

k^2=64-2k

We move all terms to the left:

k^2-(64-2k)=0

We add all the numbers together, and all the variables

k^2-(-2k+64)=0

We get rid of parentheses

k^2+2k-64=0

a = 1; b = 2; c = -64;
Δ = b2-4ac
Δ = 22-4·1·(-64)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{65}}{2*1}=\frac{-2-2\sqrt{65}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{65}}{2*1}=\frac{-2+2\sqrt{65}}{2}
$