# How do you solve 12 = 2x^2 - 5x?

Mar 29, 2018

$x = - \frac{3}{2} \text{ or } x = 4$

#### Explanation:

$\text{rearrange the equation into "color(blue)"standard form}$

$\Rightarrow 2 {x}^{2} - 5 x - 12 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{factorise using the a-c method}$

$\text{that is factors of the product } 2 \times - 12 = - 24$
$\text{which sum to - 5}$

$\text{the factors required are - 8 and + 3}$

$\text{'split' the middle term using these factors}$

$\Rightarrow 2 {x}^{2} - 8 x + 3 x - 12 = 0 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$\Rightarrow \textcolor{red}{2 x} \left(x - 4\right) \textcolor{red}{+ 3} \left(x - 4\right) = 0$

$\text{take out the common factor } \left(x - 4\right)$

$\Rightarrow \left(x - 4\right) \left(\textcolor{red}{2 x + 3}\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x - 4 = 0 \Rightarrow x = 4$

$2 x + 3 = 0 \Rightarrow x = - \frac{3}{2}$