# How do you solve 5x² - 6x – 3 = 0?

${x}_{1} = \frac{6}{10} + \frac{4 \sqrt{6}}{10} = \frac{3}{5} + \frac{2 \sqrt{6}}{5}$

${x}_{2} = \frac{6}{10} - \frac{4 \sqrt{6}}{10} = \frac{3}{5} - \frac{2 \sqrt{6}}{5}$

#### Explanation:

We can use the quadratic formula to solve for the roots of

$5 {x}^{2} - 6 x - 3 = 0$

Solution:
$5 {x}^{2} - 6 x - 3 = 0$

We make use of the constants $a = 5$ and $b = - 6$ and $c = - 3$

Now we make use of the Quadratic formula

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

$x = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(5\right) \left(- 3\right)}}{2 \left(5\right)}$

$x = \frac{+ 6 \pm \sqrt{36 + 60}}{10}$

$x = \frac{+ 6 \pm \sqrt{96}}{10}$

$x = \frac{+ 6 \pm \sqrt{16 \left(6\right)}}{10}$

$x = \frac{+ 6 \pm 4 \sqrt{6}}{10}$

${x}_{1} = \frac{6}{10} + \frac{4 \sqrt{6}}{10} = \frac{3}{5} + \frac{2 \sqrt{6}}{5}$

${x}_{2} = \frac{6}{10} - \frac{4 \sqrt{6}}{10} = \frac{3}{5} - \frac{2 \sqrt{6}}{5}$

God bless....I hope the explanation is useful.