how do you solve this?

The equation is 2x^{2}/3 - 5x/3 = 3. Let's make the coefficients integers to make life easier by multiplying through by 3. Then we move the right hand side term to the left.

2x^{2}/3 - 5x/3 = 3

2x^{2} - 5x = 9

2x^{2} - 5x - 9 = 0

Now use quadratic formula since it doesn't factor:

x = (-(-5) ± √((-5)^{2}-4*2*(-9))) / (2*2) = (5 ± √97) / 4