# How do you solve x^2+3x+1=0 using the quadratic formula?

Apr 7, 2016

Solution is given by irrational numbers $\frac{- 3 + \sqrt{5}}{2}$ and $\frac{- 3 - \sqrt{5}}{2}$.

#### Explanation:

The solution of a quadratic equation $a {x}^{2} + b x + c = 0$, using quadratic formula is given by $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Hence the solution of ${x}^{2} + 3 x + 1 = 0$ is given by

$x = \frac{- 3 \pm \sqrt{{3}^{2} - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$ or

$x = \frac{- 3 \pm \sqrt{9 - 4}}{2} = \frac{- 3 \pm \sqrt{5}}{2}$

Hence solution is given by irrational numbers $\frac{- 3 + \sqrt{5}}{2}$ and $\frac{- 3 - \sqrt{5}}{2}$.