Solve the following quadratic equation. $5 x^{2} - 4 x - 7 = 0$

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Solution

The two roots of the quadratic equation $a x^{2} + b x + c = 0$ are given by,

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

For the given equation $5 x^{2} - 4 x - 7 = 0$ ,

$b^{2} - 4 a c = (- 4)^{2} - 4 (5) (- 7) = 16 + 140 = 156$

So, the roots are,
$x = \frac{4 \pm \sqrt{156}}{2 (5)}$

$x = \frac{4 \pm 2 \sqrt{39}}{10}$

$x = \frac{2 \pm \sqrt{39}}{5}$

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