# How do you solve 5x^2 -6x +7 = 0 using the quadratic formula?

Sep 7, 2016

$x = \frac{3 - \sqrt{26}}{5} , \frac{3 + \sqrt{26}}{5}$

#### Explanation:

We have: $5 {x}^{2} - 6 x + 7 = 0$

$\implies x = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(5\right) \left(7\right)}}{2 \left(5\right)}$

$\implies x = \frac{6 \pm \sqrt{36 - 140}}{10}$

$\implies x = \frac{6 \pm \sqrt{- 104}}{10}$

$\implies x = \frac{6 \pm \sqrt{104} i}{10}$

$\implies x = \frac{6 \pm 2 \sqrt{26}}{10}$

$\implies x = \frac{3 \pm \sqrt{26}}{5}$

Therefore, the solutions to the equation are $x = 3 - \sqrt{26}$ and $x = 3 + \sqrt{26}$.