# Solve this quadratic equation using the quadratic formula. 3x^{2} + 5x + 1 = 0.

A quadratic equation is an equation that has a general form of ax^{2 }+ bx + c = 0 where a is not equal to zero. It has a degree equal to two and can have at most two solutions.

## Answer: The solutions are (-5 + √13) / 6 and (-5 - √13) / 6 for equation 3x^{2} + 5x + 1 = 0.

Let's solve step by step in detail.

**Explanation:**

Given: 3x^{2} + 5x + 1 = 0

The quadratic formula is given by x = (-b ± √ (b^{2} - 4ac)) / 2a

We know that coefficient of x^{2 } is a, coefficient of x is b and the constant is c.

Thus, for the given equation 3x^{2} + 5x + 1 = 0,

We have, a = 3, b = 5 and c = 1

Using the quadratic formula, we get,

⇒ x = -5 ± √ (5^{2 }- 4(3)(1)) / 2(3)

⇒ x = (-5 ± √13) / 6

Hence, we have two solutions:

x = (-5 + √13) / 6 and, x = (-5 - √13) / 6