# How do you find the roots of y=2x^2 – 9x + 55 using the quadratic formula?

#### Answer:

${x}_{1} = \frac{9 + \sqrt{359} i}{4} = 2.25 + 4.73682 i$

${x}_{2} = \frac{9 - \sqrt{359} i}{4} = 2.25 - 4.73682 i$

#### Explanation:

From the given equation $y = 2 {x}^{2} - 9 x + 55$

We set $y = 0$
Let $a = 2$ and $b = - 9$ and $c = 55$

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

$x = \frac{- - 9 \pm \sqrt{{\left(- 9\right)}^{2} - 4 \left(2\right) \left(55\right)}}{2 \left(2\right)}$

$x = \frac{+ 9 \pm \sqrt{81 - 440}}{4}$

$x = \frac{+ 9 \pm \sqrt{- 359}}{4}$

${x}_{1} = \frac{9 + \sqrt{359} i}{4} = 2.25 + 4.73682 i$

${x}_{2} = \frac{9 - \sqrt{359} i}{4} = 2.25 - 4.73682 i$

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