6x^3-5x^2+15x+5 / 2x^2-x+3

If you mean, (you should use parentheses)

6x^3-5x^2+15x+5 / (2x^2-x+3)

Use polynomial long division,
Here's the answer to check to your long division,

6x^3 - 5x^2 + 15x + 5/(2x^2 - x + 3)