# How do you solve 2x^2 – 3x – 5 = 0?

Aug 9, 2015

$x = - 1 , \frac{5}{2}$

#### Explanation:

Factor the equation, note that both 2 and 5 are prime numbers, therefore they can only have themselves and 1 as a factor. Therefore a factorisation of:
$2 {x}^{2} - 3 x - 5 = \left(2 x - a\right) \left(x - b\right) = 0$

Is likely.
With either $\left(\left\mid a \right\mid , \left\mid b \right\mid\right) = \left(1 , 5\right) , \left(5 , 1\right)$

By inspection we see $a = 5 , b = - 1$, therefore we have:
$2 {x}^{2} - 3 x - 5 = \left(2 x - 5\right) \left(x + 1\right) = 0 \implies x = - 1 , \frac{5}{2}$