Find the discriminant of the quadratic $3x^2 - 7x + 6.$

Solve for x:

3 x^2 - 7 x + 6 = 0

Divide both sides by 3:

x^2 - (7 x) / 3 + 2 = 0

Subtract 2 from both sides:

x^2 - (7 x) / 3 = - 2

Add 49/36 to both sides:

x^2 - (7 x) / 3 + 49/36 = - 23/36

Write the left hand side as a square:

(x - 7/6) ^2 = - 23/36

Take the square root of both sides:

x - 7/6 = (i sqrt (23)) / 6 or x - 7/6 = - (i sqrt (23)) / 6

Add 7/6 to both sides:

x = 7/6 + (i sqrt (23)) / 6 or x - 7/6 = - (i sqrt (23)) / 6

Add 7/6 to both sides:

Answer: x = 7/6 + (i sqrt (23)) / 6 or x = 7/6 - (i sqrt (23)) / 6