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

Mar 27, 2016

Solution is $x = \frac{3 - \sqrt{65}}{14}$ and $x = \frac{3 + \sqrt{65}}{14}$

#### Explanation:

According to quadratic formula, the solution of quadratic equation $a {x}^{2} + b x + c = 0$ is given by

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

As $7 {x}^{2} - 3 x = 2$ can be written in form $a {x}^{2} + b x + c = 0$ as

$7 {x}^{2} - 3 x - 2 = 0$, (i.e. $a = 7$, $b = - 3$ and $c = - 2$) and its solution will be given by

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

$x = \frac{3 \pm \sqrt{9 + 56}}{14} = \frac{3 \pm \sqrt{65}}{14}$

Hence, solution is $x = \frac{3 - \sqrt{65}}{14}$ and $x = \frac{3 + \sqrt{65}}{14}$