[tex] 3x^{2}-20x=7 \\ 3x^{2}-20x-7=0 \\ \\ x_{12}= \frac{20 \pm \sqrt{400+4*3*7} }{2*3}= \\ \\ = \frac{20 \pm \sqrt{400+4*3*7} }{2*3}= \\ \\ =\frac{20 \pm \sqrt{400+84} }{6}= \\ \\ =\frac{20 \pm \sqrt{484} }{6}=\frac{20 \pm 22 }{6} \\ \\ x_1 = \frac{20 + 22 }{6}= \frac{42}{6} =7 \\ \\ x_2 = \frac{20 - 22 }{6}= \frac{-2}{6} \;\; \text{solutie eliminata deoarece nu este naturala} \\ \\ => \text{numarul cautat este 7} [/tex]
Proba:
3 × 7² - 20 × 7 = 3 × 49 - 140 = 147 - 140 = 7
