# How do you solve 8k² - 3k =0?

Mar 26, 2016

$k = 0 \text{; } k = \frac{3}{8}$

#### Explanation:

$\textcolor{b l u e}{\text{Determining the first solution}}$

Straight away we can observe that if we set $k = 0$ then it is a
solution to the equation. To emphasise this point:
$8 \left({0}^{2}\right) - 3 \left(0\right) = 0$

This is really the same thing as suggested by mason in that
$8 \left({0}^{2}\right) - 3 \left(0\right) = 0 \text{ is equivalent to } k \left(8 k - 3\right) = 0$ where $k = 0$.

$\textcolor{b l u e}{\text{Determining the second solution}}$

$8 {k}^{2} - 3 x = 0$

Also we can write it as:$\text{ } 8 {k}^{2} = 3 k$

Divide both sides by $k$ giving

$8 k = 3$

$\implies k = \frac{3}{8}$

I nearly went on automatic and jump into using the standard formula for resolving $x$. Shows that it is worth taking the time to look hard at the question and see if you can spot any short cuts.