To solve this logarithmic equation, we can rewrite the expression inside the logarithm using the properties of logarithms.

Given:

2log₀,5 x = log₀,5 (2x² - x)

Using the power rule of logarithms, we can rewrite the left side of the equation:

log₀,5 x² = log₀,5 (2x² - x)

Now, since the logarithms are equal, we can drop the logarithm on both sides:

x² = 2x² - x

Simplify the equation by moving all terms to one side:

0 = x² - x

Now, factor the quadratic equation:

0 = x(x - 1)

Set each factor equal to zero:

x = 0, x = 1

Therefore, the solutions to the equation are x = 0 and x = 1.