15(5x-2)=82x+1


solve the extraneous root

No extraneous root here.

Just a simple equation.

opss i typed it wrong

15(5^x-2)=8^2x+1

I sent it through Wolfram the way you typed it

Even Wolfram had trouble understanding what you meant:
http://www.wolframalpha.com/input/?i=solve+15(5%5Ex-2)%3D8%5E2x%2B1

To solve the equation 15(5x-2)=82x+1 and determine if there are any extraneous roots, we need to follow these steps:

Step 1: Distribute on the left side of the equation:
75x - 30 = 82x + 1.

Step 2: Simplify the equation by combining like terms:
75x - 82x = 1 + 30,
-7x = 31.

Step 3: Divide both sides of the equation by -7 to isolate x:
-7x / -7 = 31 / -7,
x = -31/7.

After solving the equation, we find that the value of x is -31/7. However, this is the only solution to the equation, so there are no extraneous roots in this case.