k^2-8k+16=59

Solution for k^2-8k+16=59 equation:

k^2-8k+16=59

We move all terms to the left:

k^2-8k+16-(59)=0

We add all the numbers together, and all the variables

k^2-8k-43=0

a = 1; b = -8; c = -43;
Δ = b2-4ac
Δ = -82-4·1·(-43)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{59}}{2*1}=\frac{8-2\sqrt{59}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{59}}{2*1}=\frac{8+2\sqrt{59}}{2}
$