21k^2=14-7k

Solution for 21k^2=14-7k equation:

21k^2=14-7k

We move all terms to the left:

21k^2-(14-7k)=0

We add all the numbers together, and all the variables

21k^2-(-7k+14)=0

We get rid of parentheses

21k^2+7k-14=0

a = 21; b = 7; c = -14;
Δ = b2-4ac
Δ = 72-4·21·(-14)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-35}{2*21}=\frac{-42}{42}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+35}{2*21}=\frac{28}{42}
=2/3
$