Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ .

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Solution

$\Rightarrow$ The given quadratic equation is $5 x^{2} - 6 x - 2 = 0$ , comparing it with $a x^{2} + b x + c = 0$
$\Rightarrow$ We get, $a = 5, b = - 6, c = - 2$
$\Rightarrow$ $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$= \frac{- (- 6) \pm \sqrt{(- 6)^{2} - 4 (5) (- 2)}}{2 (5)}$

$= \frac{6 \pm \sqrt{36 + 40}}{10}$

$= \frac{6 \pm \sqrt{76}}{10}$

$= \frac{6 \pm 2 \sqrt{19}}{10}$

$= \frac{3 \pm \sqrt{19}}{5}$

$x = \frac{3 + \sqrt{19}}{5}$ and $x = \frac{3 - \sqrt{19}}{5}$

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5 x^{2} - 6 x - 2 = 0

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