[tex]x(12 - x) = 32 \\ 12x - {x}^{2} = 32 \\ - {x}^{2} + 12x - 32 = 0 \\ D = {b}^{2} - 4ac = {12}^{2} - 4 \times ( - 1) \times ( - 32) = 16 \\ x_{1} = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 12 - \sqrt{16} }{2 \times ( - 1)} = 8 \\ x_{2} = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 12 + \sqrt{16} }{2 \times ( - 1)} = 4[/tex]