k^2-100=84

Solution for k^2-100=84 equation:

k^2-100=84

We move all terms to the left:

k^2-100-(84)=0

We add all the numbers together, and all the variables

k^2-184=0

a = 1; b = 0; c = -184;
Δ = b2-4ac
Δ = 02-4·1·(-184)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*1}=\frac{0-4\sqrt{46}}{2}
=-\frac{4\sqrt{46}}{2}
=-2\sqrt{46}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*1}=\frac{0+4\sqrt{46}}{2}
=\frac{4\sqrt{46}}{2}
=2\sqrt{46}
$