# What are the exact solutions of x^2-x-4=0?

Nov 16, 2016

The solutions are $S = \left\{2.56 , - 1.56\right\}$

#### Explanation:

The equation is ${x}^{2} - x - 4 = 0$

Let's calculate the discriminant

$\Delta = {b}^{2} - 4 a c = {\left(- 1\right)}^{2} - 4 \cdot 1 \cdot \left(- 4\right) = 17$

As $\Delta > 0$, we have 2 real roots

$x = \frac{- b \pm \sqrt{\Delta}}{2 a} = \frac{1 \pm \sqrt{17}}{2}$

Therefore,

${x}_{1} = \frac{1 + \sqrt{17}}{2} = 2.56$

and ${x}_{2} = \frac{1 - \sqrt{17}}{2} = - 1.56$