6k^2=20k-k^2

Solution for 6k^2=20k-k^2 equation:

6k^2=20k-k^2

We move all terms to the left:

6k^2-(20k-k^2)=0

We get rid of parentheses

6k^2+k^2-20k=0

We add all the numbers together, and all the variables

7k^2-20k=0

a = 7; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·7·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*7}=\frac{0}{14}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*7}=\frac{40}{14}
=2+6/7
$