How do you solve 5x^2 - 7x - 3 = 0 using the quadratic formula?

Mar 31, 2018

$x = \frac{7 + \sqrt{109}}{10}$ or $\frac{7 - \sqrt{109}}{10}$

Explanation:

Quadratic formula gives the solution of $a {x}^{2} + b x + c = 0$ as $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

As in $5 {x}^{2} - 7 x - 3 = 0$, $a = 5$, $b = - 7$ and $c = - 3$

$x = \frac{- \left(- 7\right) \pm \sqrt{{\left(- 7\right)}^{2} - 4 \cdot 5 \cdot \left(- 3\right)}}{2 \cdot 5}$

= $\frac{7 \pm \sqrt{49 + 60}}{10}$

i.e. $x = \frac{7 + \sqrt{109}}{10}$ or $\frac{7 - \sqrt{109}}{10}$