To find the quadratic equation that has 6 and 8 as its solutions, we can use the fact that a quadratic equation with roots \( r_1 \) and \( r_2 \) can be expressed in the form:
\[ f(x) = (x - r_1)(x - r_2) \]
For this case, the roots are \( r_1 = 6 \) and \( r_2 = 8 \). Plugging these values into the equation, we get:
\[ f(x) = (x - 6)(x - 8) \]
Next, we expand this expression:
\[ f(x) = x^2 - 8x - 6x + 48 \] \[ f(x) = x^2 - 14x + 48 \]
Thus, the quadratic equation that has 6 and 8 as its solutions is:
\[ x^2 - 14x + 48 = 0 \]