Question

determine a raiz da equação a seguir 1/6.(5x-2)+1/9.(4x+7)=1/18x+2

Answer 1

$\frac{1}{6} (5x - 2) + \frac{1}{9} (4x + 7) = \frac{1}{18x + 2} \\ \frac{5x}{6} - \frac{2}{6} + \frac{ 4x }{9} + \frac{7}{9} = \frac{1}{18x + 2} \\ \frac{5x}{6} + \frac{4x}{9} - \frac{1}{18x + 2} = \frac{2}{6} - \frac{7}{9} \\ \frac{5x \times 3(9x + 1)}{18(9x + 1)} + \frac{4x \times 2(9x + 1)}{18(9x + 1)} - \frac{1 \times 9}{18(9x + 1)} = \frac{6}{18} - \frac{14}{18} \\ \frac{15x(9x + 1) + 8x(9x + 1) - 9}{18(9x + 1)} = - \frac{8}{18} \\ \frac{135 {x}^{2} + 15x + 72 {x}^{2} + 8x - 9 }{9x + 1} = - 8 \\ 207 {x}^{2} + 23x - 9 = - 8(9x +1 ) \\ 207 {x}^{2} + 23x - 9 = - 72x - 8 \\ 207 {x}^{2} + 95x - 1 = 0 \\ \boxed{x = \frac{ - 95 + \sqrt{9853} }{414} \: ou \: x = \frac{ - 95 - \sqrt{9853} }{414} }$