Verified answer

3x^2 - 4x - 10 = 0

3(x^2 - 4/3) = 10

3(x - 4/6)^2 = 10

3(x - 2/3)^2 = 10 + 3(4/9)

3(x - 2/3)^2 = 10 + 12/9

3(x - 2/3)^2 = 102/9

(x - 2/3) = sqrt(102/27)

x = +/- sqrt(102/27) + 2/3

x = +/- sqrt(2*17*3/9*3) + 2/3

x = +/- sqrt(34)/3 + 2/3

You can't solve this by completing the square because x is not a rational number. But you can use the quadratic equation, which will give the answer:

4 +/- the square root of the quantity (4^2-4*3*(-10)), all divided by 2*3. This equals approximately 2.61 or -1.28, or the same quantity found by Philo above.

3x² - 4x = 10

x² - (4/3)x = 10/3 .......... add the square of half of the 4/3, (2/3)² = 4/9

x² - (4/3)x + 4/9 = 10/3 + 4/9

(x - 2/3)² = 34/9

x - 2/3 = ±√34 / 3

x = (2 ± √34) / 3

x(3x-4)=10

x=10

3x-4=10

3x=14

x=14/3