16k+k^2=60

Solution for 16k+k^2=60 equation:

16k+k^2=60

We move all terms to the left:

16k+k^2-(60)=0

a = 1; b = 16; c = -60;
Δ = b2-4ac
Δ = 162-4·1·(-60)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{31}}{2*1}=\frac{-16-4\sqrt{31}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{31}}{2*1}=\frac{-16+4\sqrt{31}}{2}
$