(x:2)-10=x:3

To solve the equation \((x:2) - 10 = x:3\), we can rewrite it without using the colon notation:

Let \(x:2\) denote \(\frac{x}{2}\) and \(x:3\) denote \(\frac{x}{3}\). The equation then becomes:

\[ \frac{x}{2} - 10 = \frac{x}{3} \]

Now, to eliminate the fractions, we can find a common denominator. The least common multiple of \(2\) and \(3\) is \(6\). We'll multiply every term by \(6\):

\[ 6 \left(\frac{x}{2}\right) - 6(10) = 6 \left(\frac{x}{3}\right) \]

This simplifies to:

\[ 3x - 60 = 2x \]

Now, we will isolate \(x\) by subtracting \(2x\) from both sides:

\[ 3x - 2x - 60 = 0 \]

Which simplifies to:

\[ x - 60 = 0 \]

Now, add \(60\) to both sides:

\[ x = 60 \]

Thus, the solution to the equation is:

\[ \boxed{60} \]