Inverse and 2 Word Problems (Algebra 2)

I'm having a hard time with this inverse problem and I'm not sure whether I have completely found the inverse or if I did something wrong.

Find inverse: y= 4x^2 - 10x

This is what I have done so far step by step

x= 4y^2 - 10y

0= 4y^2 - 10y - x

Then set up quadratic formula (used power of 1/2 because i don't know how to put sq root on here)

10 +(-10^2 - 4(4)(-x))^(1/2)/8

10 +(100 + 16x)^(1/2)/8 This is where I got stuck

Edit:

Ran into more trouble with 2 word problems:

1st problem

Write an equation that can be used to solve the problem. The answer the question asked. A group of college students are volunteering for habitat for humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Kathy can paint a certain room in 4 hours. Rhonda can paint the same room in 6 hours. How long will it take them working together to paint the room?

2nd problem

The sum of the reciprocal of a number and the reciprocal of 6 less than the number is 8 times the reciprocal of the original number. Find the original number.