This can be solved using Newton’s Method. All three zeroes can be found.
Another method (not using calculus) can be used to find one zero only.
If you are using calculus, differentiate the expression: 3x²-19.
Evaluating x-(x³-19x+3)/(3x²-19) starting with x=0. Plug the answer back into x and perform the expression again. You will need a calculator. Repeat until you get a stable result. This is Newton’s approximation for a zero close to 0. If you plot the graph of the function roughly you will see two other zeroes at about -5 and 5. Starting with these repeat the above procedure to find each of the zeroes: 0.1581027374, -4.435799312, 4.277696575 approx depending on the resolution of your calculator.
19x=x³+3, x=(x³+3)/19 can be used to find the zero close to 0. Apply the iteration for successive values of x.