k2+20=80

Solution for k2+20=80 equation:

k2+20=80

We move all terms to the left:

k2+20-(80)=0

We add all the numbers together, and all the variables

k^2-60=0

a = 1; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·1·(-60)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*1}=\frac{0-4\sqrt{15}}{2}
=-\frac{4\sqrt{15}}{2}
=-2\sqrt{15}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*1}=\frac{0+4\sqrt{15}}{2}
=\frac{4\sqrt{15}}{2}
=2\sqrt{15}
$