# How do you find the roots, real and imaginary, of y= 2x^2 - 3x + 2  using the quadratic formula?

${x}_{1} = \frac{3 + \sqrt{7} i}{4}$

${x}_{2} = \frac{3 - \sqrt{7} i}{4}$

#### Explanation:

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

we have to identify correctly our real number coefficients a, b ,c

set y=0

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

let $a = 2$ and $b = - 3$ and $c = 2$

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

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

${x}_{1} = \frac{3 + \sqrt{7} i}{4}$

${x}_{2} = \frac{3 - \sqrt{7} i}{4}$

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