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
