Can someone please help me with this one?

Solve (5x+4)^1/2-3x=0

Just so you know, it is to the 1/2 power.

Add 3x to both sides of the equation, then square both sides.

That should enable you to gather terms and factor.

Yeah, that's the part I understood. Could you help me with the factoring?

This is what I have as of now:
(5x+4)^1/2-3x=0
5x+4=3x^2

3x^2-5x-4=0
Go to the quadratic equation

x= -b +- sqrt (b^2=4ac) /2a

x= 5 +- sqrt (25+48) /6

x= 5 +- sqrt (73) /6

x= -0.590667291 ; x= 2.25733396

check my work.

Oh, really? We didn't learn about doing it like that, but I think it does work. Thanks!

wait, I got the same answers as you, but then I checked my work and neither worked

dang: error
(5x+4)^1/2-3x=0
5x+4=Mb>9x^2

typo
(5x+4)^1/2-3x=0
5x+4= 9x^2

That changes the quadratic to

9x^2 -5x -4=0

x= ( 5 +- sqrt (25 + 36*4))/18

check that.

yes it works! thanks a ton!

You're welcome! I'm glad it worked for you. Just to clarify, here are the steps to solve the equation (5x+4)^(1/2) - 3x = 0:

1. Add 3x to both sides of the equation:
(5x+4)^(1/2) = 3x

2. Square both sides of the equation to eliminate the square root:
[(5x+4)^(1/2)]^2 = (3x)^2
5x + 4 = 9x^2

3. Rearrange the equation to get a quadratic form:
9x^2 - 5x - 4 = 0

4. Use the quadratic formula to find the solutions:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 9, b = -5, and c = -4. Plugging them into the formula, we have:
x = (-(-5) ± √((-5)^2 - 4*9*(-4))) / (2*9)
Simplifying, we get:
x = (5 ± √(25 + 144)) / 18
x = (5 ± √169) / 18
x = (5 ± 13) / 18

5. Simplify the solutions:
The two solutions are x = (5 + 13) / 18 = 18/18 = 1 and x = (5 - 13) / 18 = -8/18 = -4/9.

Remember to always double-check your work to ensure accuracy.