# How do you find the roots, real and imaginary, of y=2x² -452x-6  using the quadratic formula?

Jul 11, 2017

$x = 113 \pm 2 \sqrt{3193}$

#### Explanation:

$y = 2 {x}^{2} - 452 - 6$

Let $y = 0$

$2 {x}^{2} - 452 - 6 = 0$

${x}^{2} - 226 - 3 = 0$

$x = \frac{226 \pm \sqrt{{226}^{2} - 4 \left(1\right) \left(3\right)}}{2} = \frac{226 \pm 4 \sqrt{3193}}{2}$

$= 113 \pm 2 \sqrt{3193}$