[tex](a + 2) {x}^{2} - (2a + 7)x + a + 7= 0 \\ x = \frac{1}{3} \\ (a +2 ) \times ( \frac{1}{3} ) {}^{2} - (2a + 7) \times \frac{1}{3} + a + 7 = 0 \\ (a + 2) \times \frac{1}{9} - (2a + 7) \times \frac{1}{3} + a + 7 = 0 \: \: | \times 9 \\ a + 2 - 3(2a + 7) +9 a + 63 = 0 \\ 10a + 65- 6a - 21 = 0 \\ 4a + 44 = 0 \\ 4a = - 44 \\ a = - 44 \div 4 \\ a = - 11[/tex]