Question

$\frac{2}{x} - \frac{x + 1}{5} = - \frac{4}{5}$
transform to quadratic equation.
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Answer 1

Given :

$\sf\dfrac{2}{x} - \dfrac{x + 1}{5} = - \dfrac{4}{5}$

To find :

• Quadratic equation ( by transforming the given expression )

Solution :

$\implies\sf\dfrac{2}{x} - \dfrac{x + 1}{5} = - \dfrac{4}{5}$

LCM of x and 5 = 5x

$\implies\sf \dfrac{10 - ( {x}^{2} + x)}{5x} = - \dfrac{4}{5}$

$\implies\sf \dfrac{10 - {x}^{2} - x}{5x} = - \dfrac{4}{5}$

$\implies\sf{10 - {x}^{2} - x} = - \dfrac{4}{5} \times {5x}$

$\implies\sf{10 - {x}^{2} - x} = - \dfrac{4}{1} \times {x}$

$\implies\sf{10 - {x}^{2} - x} = - {4x}$

$\implies\sf{10 - {x}^{2} - x} + 4x = 0$

Taking out -1 common.

$\implies\sf{ - 10 + {x}^{2} + x} - 4x = 0$

$\implies\sf{ {x}^{2} } - 3x - 10= 0$

Answer :

$\sf{ {x}^{2} } - 3x - 10= 0$