120k^2-84=0

Solution for 120k^2-84=0 equation:

120k^2-84=0

a = 120; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·120·(-84)
Δ = 40320
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:

$\sqrt{\Delta}=\sqrt{40320}=\sqrt{576*70}=\sqrt{576}*\sqrt{70}=24\sqrt{70}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{70}}{2*120}=\frac{0-24\sqrt{70}}{240}
=-\frac{24\sqrt{70}}{240}
=-\frac{\sqrt{70}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{70}}{2*120}=\frac{0+24\sqrt{70}}{240}
=\frac{24\sqrt{70}}{240}
=\frac{\sqrt{70}}{10}
$