SOLUTION: How do I solve 2/3x = the square root of 24x

SOLUTION: How do I solve 2/3x = the square root of 24x - 128?

Question 85363This question is from textbook ALGEBRA 1
: How do I solve 2/3x = the square root of 24x - 128? This question is from textbook ALGEBRA 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
How do I solve 2/3x = the square root of 24x - 128?
This problem, as written, is ambiguous, a few brackets would do wonders:
Do you mean:
= - 128
or
= - 128
or
=
:
The last has integer solutions, so will assume that is it:
:
Multiply equation by 3 and get rid of the denominator:
2x = 3*
:
Square both sides and you have:
4x^2 = 9(24x-128)
:
4x^2 = 216x - 1152
:
4x^2 - 216x + 1152 = 0; arrange as a quadratic equation
:
Simplify, divide equation by 4
x^2 - 54x - 288 = 0
:
Factors to:
(x - 48)(x - 6) = 0
:
Solutions are: x = +6 and x = +48
:
You should check both solutions in the original equation
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