solving polynomial with degree 3...

the problem is...

$\displaystyle -x^3+12x^2-47x+24=0$

This polynomial was created for a word problem. The problem started off w/ this guy that had a block of ice 3x4x5=60 ft^3

He wants to reduce the volume TO (3/5) the original volume by **removing the same # of feet from each dimension.**

I made the equation... $\displaystyle (3-x)(4-x)(5-x)=V(x)$ to represent the volume of the cube in terms of the amount of feet removed. After multiplying out this problem becomes $\displaystyle V(x)=-x^3+12x^2-47x+60$

Since he wants to reduce the volume TO (3/5) the original volume, I can say that...

$\displaystyle (3/5)\cdot60=-x^3+12x^2-47x+60$

OR

$\displaystyle 0=-x^3+12x^2-47x+24$

You can see this is the same polynomial that appears at the beginning of this post. I tried to find a whole number root (positive in this case only) and couldn't find one. I know the answer is ABOUT .6 feet. So, it makes sense that I can't plug in positive factors of 24 into the equation and get zero. Obviously, taking all the factors of 24 where one factor is a fraction is an absurd notion.

I can't use the quadratic formula for this problem either, since this polynomial is not a quadratic function. It has a constant, so it's not like I can remove x from the polynomial.

Any idea how I might solve this problem?