Rewrite: 3x²-7sin(x)+2=0
The derivative of this is: 6x-7cos(x).
We can use Newton’s Method to find x.
If we plot y=3x²-7sin(x)+2 we can find x intercepts representing the solutions.
Then we apply the iterative formula:
x=x-(3x²-7sin(x)+2)/(6x-7cos(x)), where a starting value of x is plugged into the expression on the right of equals, then the result is plugged into the same expression iteratively until a stable value is obtained.
If we start with x=0 (y=2), after just a few iterations, and using a calculator we find a solution close to 0: x=0.3427244.
If we start with x=1, we find x=1.2414854.
So to an accuracy of 7 decimal places, x=0.3427244 or 1.2414854.