Question

A tangent to the parabola y=3x^2-7x+5 is perpendicular to the x+5y-10=0. Determine the equation of the tangent

Answer 1

This is a good problem, lots of parts to consider. :)
You're given a parabola and a line that is perpendicular to its tangent line.
I would suggest finding out where that perpendicular line intersects the parabola first.
Once you know that, you know the point of tangency.