finding the value of u of equation 5u^2 = 10u

Question

I was solving a question, and while solving that problem I noticed something

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$5u^2 = 10u$

(solving this) this can be solved as:

$5 \cdot u \cdot u = 10 \cdot u$

$u = \dfrac{10u}{5u}$

$u = 2$

so my answer was $2$

but at the same time I solved this like bellow:

$5u^2 = 10u$

$u^2 = \dfrac{10u}{5}$

(under rooting both sides )

$u = \sqrt{\dfrac{10u}{5}}$

Now the value of this $u$ is $2$ and $\sqrt{\dfrac{10u}{5}}$ that is the value of $u$ is different. so can you tell me which value is right

or

which method is correct to find the value of $u$

Answer 1

Firstly when you write $u^2 = \dfrac{10u}{5}$ then this will imply $u = \pm\sqrt{\dfrac{10u}{5}}$ and then since $u$ is in the square root it has to be positive. That is why we have to take $u=+\sqrt{\dfrac{10u}{5}}$. You can either check by trial and erorr that for $u=0$ and $u=2$ the equation is true.
Secondly there is nothing wrong with $u = \sqrt{\dfrac{10u}{5}}$, you are just expressing $u$ in terms of itself. For finding the value of $u$ analytically you have to solve the quardratic equation as the answer above mine's has shown.

Answer 2

$$5u^2 - 10 u = 0 \implies 5u(u-2) = 0 \implies u = 0, u = 2$$