To find the quadratic equation that has 6 and 8 as its solutions, we can use the fact that if \( r_1 \) and \( r_2 \) are the roots of a quadratic equation, the equation can be expressed in the form:
\[ (x - r_1)(x - r_2) = 0 \]
In this case, \( r_1 = 6 \) and \( r_2 = 8 \). Thus, we can write:
\[ (x - 6)(x - 8) = 0 \]
Now, expanding this:
\[ x^2 - 8x - 6x + 48 = 0 \]
Combining the terms:
\[ x^2 - 14x + 48 = 0 \]
Therefore, the quadratic equation we are looking for is:
\[ x^2 - 14x + 48 = 0 \]