# How do you find the roots, real and imaginary, of y=-15^2 +40x -34  using the quadratic formula?

## How do you find the roots, real and imaginary, of $y = - 15 {x}^{2} + 40 x - 34$ using the quadratic formula?

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

#### Explanation:

Where:
$a = - 15$
$b = 40$
$c = - 34$

$\therefore x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{- \left(40\right) \pm \sqrt{{\left(40\right)}^{2} - 4 \left(- 15\right) \left(- 34\right)}}{2 \left(- 15\right)}$
$x = \frac{- 40 \pm \sqrt{- 440}}{- 30}$

And because one cannot square root any negative integers,
the answer obtained for $y = - 15 {x}^{2} + 40 x - 34$ would remain as:
$x = \frac{- 40 \pm \sqrt{- 440}}{- 30}$

By presenting the roots:
$x = \frac{- 40 + \sqrt{- 440}}{- 30}$ and $x = \frac{- 40 - \sqrt{- 440}}{- 30}$