7k^2=k+14

Solution for 7k^2=k+14 equation:

7k^2=k+14

We move all terms to the left:

7k^2-(k+14)=0

We get rid of parentheses

7k^2-k-14=0

We add all the numbers together, and all the variables

7k^2-1k-14=0

a = 7; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·7·(-14)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{393}}{2*7}=\frac{1-\sqrt{393}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{393}}{2*7}=\frac{1+\sqrt{393}}{14}
$