100-12k^2=0

Solution for 100-12k^2=0 equation:

100-12k^2=0

a = -12; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-12)·100
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*-12}=\frac{0-40\sqrt{3}}{-24}
=-\frac{40\sqrt{3}}{-24}
=-\frac{5\sqrt{3}}{-3}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*-12}=\frac{0+40\sqrt{3}}{-24}
=\frac{40\sqrt{3}}{-24}
=\frac{5\sqrt{3}}{-3}
$