Final answer:
The original 4th root equation can be squared to remove the 4th root, yielding a quadratic equation in the form ax^2+bx+c=0, which is then solved for x using the quadratic formula. The correct option will be the value of x that makes the original equation true.
Step-by-step explanation:
The equation given is the 4th root of (3-8x)2 equals 2x, which can be approached by first squaring both sides to get rid of the 4th root. Squaring 2x, we get 4x2. Next, we need to square the entire left side of the equation, (3-8x)2, which is already squared, thus leaving it as is. Now, the equation is simplified to 3-8x=4x2.
Now, rearranging it into a quadratic equation, we get 4x2 + 8x - 3 = 0. This quadratic equation can be solved using the quadratic formula x = (-b ± √(b2 - 4ac)) / (2a), where a=4, b=8, and c=-3. Upon solving, we find the values of x that satisfy the equation.
To verify the solutions, we substitute each option back into the original equation and check for equality. The correct option will be the value of x that makes the original equation true.