k^2-16k=63

Solution for k^2-16k=63 equation:

k^2-16k=63

We move all terms to the left:

k^2-16k-(63)=0

a = 1; b = -16; c = -63;
Δ = b2-4ac
Δ = -162-4·1·(-63)
Δ = 508
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:

$\sqrt{\Delta}=\sqrt{508}=\sqrt{4*127}=\sqrt{4}*\sqrt{127}=2\sqrt{127}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{127}}{2*1}=\frac{16-2\sqrt{127}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{127}}{2*1}=\frac{16+2\sqrt{127}}{2}
$