Question

7x/6 - 30/x = x/3 find quadratic equations.

Answer 1

7x / 6 - 30 /x = x /3

7x² - 180 / 6x = x /3

3(7x² - 180) = 6x²

7x² - 180 = 6x² / 3

7x² - 180 = 2x²

7x² - 2x² = 180

5x² = 180

x² = 180 / 5

x² = 36

x = 6

Hence

x = 6

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Answer 2

$\red {\huge{ \underline{ \overline{ \mid{ \bold {\purple{ \: \:SOLUTION \: \: \red{ \mid}}}}}}}}$

$\bold{ \: \: \: \: \: \: \: \: \: \frac{7x}{6} - \frac{30}{x} = \frac{x}{3} } \\ \\ \bold{ \Longrightarrow \: \frac{7x {}^{2} - 180}{6x} = \frac{x}{3} } \\ \\ \bold{ \Longrightarrow \: 3(7x {}^{2} - 180) = x \times 6x } \\ \\ \bold{ \Longrightarrow \: 21x {}^{2} - 540 = 6x{}^{2}} \\ \\ \bold{ \Longrightarrow \: 21x {}^{2} - 6x{}^{2} - 540= 0} \\ \\ \bold{\Longrightarrow \: 15x {}^{2} - 540 = 0} \\ \\ \bold{\Longrightarrow \: x {}^{2} - 36 = 0 }$

$\underline{ \bold{ \: \: The \: \: quadratic \: \: equation \: \: is \: : }} \\ \\ \boxed{ \boxed{ \bold{ \red{ \: \: x {}^{2} - 36 = 0 \: \: Or , \: \: x {}^{2} - 0.x - 36 = 0}}}}$

$\bold{Now , }$

$\bold{x {}^{2} - 36 = 0} \\ \\ \bold{\Longrightarrow \: x {}^{2} = 36} \\ \\ \bold{\Longrightarrow \: x = \sqrt {\:36\: }}\\ \\ \bold{\therefore \: \: x = \: \pm \: \: 6 }$

$\bold{\therefore \: \: The \: \:roots \: \: of \: \: the \: \: quadratic \:\: } \\ \\ \bold{equation \: \: are \: \: : \red{\: \: x = 6 \: \: \: Or , \: \: \: x = - 6 } \:. }$