Question

x ao quadrado menos 4x/12= 5/6
${x}^{2} - \frac{4x}{12} = \frac{5}{6}$
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Answer 1

$x^{2} - \frac{4x}{12} = \frac{5}{6}$

$x^{2} - \frac{4x}{12} - \frac{5}{6} = 0$

Trata-se de uma equação de segundo grau. Primeiro, precisamos definir os coeficientes, calcular o delta (D), e em seguida, usando a fórmula de bháskara, calcular as raízes reais de x.

Coeficientes:

$a = 1\\\\b = \frac{-4}{12} = \frac{-1}{3} \\\\c = \frac{-5}{6}$

$D = b^{2} - 4ac\\\\D = (\frac{-1}{3}) ^{2} - 4 * 1 * (-\frac{5}{6}) \\\\D = \frac{1}{9} + \frac{20}{6}\\\\D = \frac{2+60}{18}\\\\D = \frac{62}{18}\\\\D = 3,4444...$

$x = \frac{-b + ou - \sqrt{D} }{2a}\\\\x = \frac{-(-\frac{1}{3}) + ou - \sqrt{3,4444...}  }{2*1}\\\\x = \frac{\frac{1}{3} + ou - 1,855  }{2}\\\\\\x1 = \frac{\frac{1}{3} + 1,855}{2}\\\\x1 = \frac{\frac{5,565+1}{3} }{2}\\\\x1 = \frac{6,565*2}{3}\\\\x1 = 4,376$

$x2 = \frac{\frac{1}{3} - 1,855}{2}\\\\x2 = \frac{\frac{1-5,565}{3} }{2}\\\\x2 = \frac{-4,565*2}{3}\\\\x2 = -3,043$

x ≅ {4,376; -3,043}

Espero ter ajudado. Me avise se houver algum erro.