#### Answer

$n = 5.236, 0.764$

#### Work Step by Step

$4(n-3)^{2} + 10 = 30$
$4[n(n-3)-3(n-3)] = 30 - 10$
$4[n^{2} - 3n - 3n + 9] = 20$
$4[n^{2} - 6n + 9] = 20$
$4n^{2} - 24n + 36 = 20$
$4n^{2} - 24n + 36 - 20 = 0$
$4n^{2} - 24n + 16 = 0$
$4(n^{2} - 6n + 4) = 0$
$n = \frac{-(-6)±\sqrt {(-6)^{2}-4(1)(4)}}{2(1)}$
$n = \frac{6±\sqrt {36-4(1)(4)}}{2}$
$n = \frac{6±\sqrt {36-16}}{2}$
$n = \frac{6±\sqrt {20}}{2}$
$n = \frac{6±2\sqrt {5}}{2}$
$n = \frac{3±\sqrt {5}}{1}$
$n = 3±\sqrt {5}$
$n = 5.236, 0.764$