In the following equation, find the value of k for which the given value is a solution of the given equation, the value of k is
$7 x^{2} + k x - 3 = 0, x = 2 / 3$

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Solution

Given equation in
$7 x^{2} + k x - 3 = 0, x = 2 / 3$
$x = 2 / 3$ is the solution of Given equation only if it satisfy the equation.
$7 {(\frac{2}{3})}^{2} + k . (\frac{2}{3}) - 3 = 0$
$\Rightarrow 7 (\frac{4}{9}) + k (\frac{2}{3}) - 3 = 0$
$\Rightarrow \frac{2 k}{3} = 3 - 28 / 9 \Rightarrow k = \frac{- 1}{6}$

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