# Thread: Solving For Non-Integer Bases

1. ## Solving For Non-Integer Bases

Hello there first-time poster here!

First of all, my apologies if this is the wrong forum to post in, my question pertains to a computer science math class, but I'm not quite sure which discipline of math it falls under.

Anywho, my question is, how can you solve for a non-integer number base, given everything but said base itself?

I have a number in base 10, (84) and a number in base b (234) and I have to solve for b. 8410 = 234b

If anyone could point me in the right direction on how to solve this, I would be very thankful.

2. ## Re: Solving For Non-Integer Bases

Hello, rlp22!

I have a number 84 in base 10, and a number in base b (234) and I have to solve for b.
. . 8410 = 234b

If anyone could point me in the right direction on how to solve this, I would be very thankful.
$\displaystyle \text{Recall that }234_b\text{ means }2b^2 + 3b + 4$
$\displaystyle \text{So we have: }\:2b^2 + 3b + 4 \:=\:84 \quad\Rightarrow\quad 2b^2 + 3b - 80 \:=\:0$
Quadratic Formula: .$\displaystyle b \;=\;\dfrac{-3 \pm\sqrt{649}}{4}$