x2+6=5x

To solve the equation \( x^2 + 6 = 5x \), we first rearrange the equation to set it to zero:

\[ x^2 - 5x + 6 + 6 - 6 = 0 \] \[ x^2 - 5x + 6 = 0 \]

Now, we can factor the quadratic equation:

\[ (x - 2)(x - 3) = 0 \]

Setting each factor to zero gives us the possible solutions for \( x \):

1. \( x - 2 = 0 \) → \( x = 2 \)
2. \( x - 3 = 0 \) → \( x = 3 \)

Thus, the solutions to the equation \( x^2 + 6 = 5x \) are:

\[ x = 2 \quad \text{and} \quad x = 3 \]