65Solving f(a)=21 for a quadratic

The function $\displaystyle f$ is defined by $\displaystyle f(x) = x^2 + 4x$. For what positive value of $\displaystyle a$ does $\displaystyle f(a) = 21$?

The positive value is a = 3. Setting a² + 4a = 21 gives a² + 4a − 21 = 0, which factors as (a+7)(a−3) = 0, so a = −7 or 3; the positive one is 3. Check: 3² + 4(3) = 9 + 12 = 21.