[tex]given \: equation: {x}^{2} - 9x + 3 = 0 \\ \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x = \frac{ 9 \pm \sqrt{ {( - 9)}^{2} - 4 \times 1 \times 3} }{2 \times 1} \\ \\ x = \frac{9 \pm \sqrt{81 - 12} }{2} \\ \\ x = \frac{9 \pm \sqrt{69} }{2} \\ \\ x = \frac{9 + \sqrt{69} }{2} \: \: and \: \: \frac{9 - \sqrt{69} }{2}[/tex]
