Solve this quadratic equation using the quadratic formula.

3x^2 + 5x + 1 = 0 the answer is a fraction with a nominator with a root

Solve for x over the real numbers:

3 x^2 + 5 x + 1 = 0

Divide both sides by 3:

x^2 + (5 x) / 3 + 1/3 = 0

Subtract 1/3 from both sides:

x^2 + (5 x) / 3 = - 1/3

Add 25/36 to both sides:

x^2 + (5 x) / 3 + 25/36 = 13/36

Write the left hand side as a square:

(x + 5/6) ^2 = 13/36

Take the square root of both sides:

x + 5/6 = sqrt (13) / 6 or x + 5/6 = - sqrt (13) / 6

Subtract 5/6 from both sides:

x = sqrt (13) / 6 - 5/6 or x + 5/6 = - sqrt (13) / 6

Subtract 5/6 from both sides:

Answer: x = sqrt (13) / 6 - 5/6 or x = - 5/6 - sqrt (13) / 6