3k^2=k(5-2k)

Solution for 3k^2=k(5-2k) equation:

3k^2=k(5-2k)

We move all terms to the left:

3k^2-(k(5-2k))=0

We add all the numbers together, and all the variables

3k^2-(k(-2k+5))=0


We calculate terms in parentheses: -(k(-2k+5)), so:

k(-2k+5)

We multiply parentheses

-2k^2+5k

Back to the equation:

-(-2k^2+5k)


We get rid of parentheses

3k^2+2k^2-5k=0

We add all the numbers together, and all the variables

5k^2-5k=0

a = 5; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·5·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*5}=\frac{0}{10}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*5}=\frac{10}{10}
=1
$