6k^2+5=269

Solution for 6k^2+5=269 equation:

6k^2+5=269

We move all terms to the left:

6k^2+5-(269)=0

We add all the numbers together, and all the variables

6k^2-264=0

a = 6; b = 0; c = -264;
Δ = b2-4ac
Δ = 02-4·6·(-264)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{11}}{2*6}=\frac{0-24\sqrt{11}}{12}
=-\frac{24\sqrt{11}}{12}
=-2\sqrt{11}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{11}}{2*6}=\frac{0+24\sqrt{11}}{12}
=\frac{24\sqrt{11}}{12}
=2\sqrt{11}
$