5k^2-8K=21

Solution for 5k^2-8K=21 equation:

5k^2-8=21

We move all terms to the left:

5k^2-8-(21)=0

We add all the numbers together, and all the variables

5k^2-29=0

a = 5; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·5·(-29)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{145}}{2*5}=\frac{0-2\sqrt{145}}{10}
=-\frac{2\sqrt{145}}{10}
=-\frac{\sqrt{145}}{5}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{145}}{2*5}=\frac{0+2\sqrt{145}}{10}
=\frac{2\sqrt{145}}{10}
=\frac{\sqrt{145}}{5}
$