7k^2+1=4K

Solution for 7k^2+1=4K equation:

7k^2+1=4

We move all terms to the left:

7k^2+1-(4)=0

We add all the numbers together, and all the variables

7k^2-3=0

a = 7; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·7·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*7}=\frac{0-2\sqrt{21}}{14}
=-\frac{2\sqrt{21}}{14}
=-\frac{\sqrt{21}}{7}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*7}=\frac{0+2\sqrt{21}}{14}
=\frac{2\sqrt{21}}{14}
=\frac{\sqrt{21}}{7}
$