# How do you find the roots, real and imaginary, of y= 8x^2-15x-4-2(3x+3)^2  using the quadratic formula?

Jan 12, 2016

$x \approx - 4.83$ or $x \approx - 0.27$

#### Explanation:

First multiply out the terms so that the expression can be rearranged into standard form.
$y = 8 {x}^{2} - 15 x - 4 - 2 \left(9 {x}^{2} + 18 x + 9\right)$
$y = 8 {x}^{2} - 18 {x}^{2} - 15 x - 36 x - 4 - 9$
$y = - 10 {x}^{2} - 51 x - 13$
For a quadratic expression $y = a {x}^{2} + b x + c$ the quadratic formula is x=(-b+-sqrt(b^2-4ac))/(2a
x = (-(-51)+-sqrt((-51)^2 -4(-10)(-13)))/(2(-10)
$x = \frac{51 \pm \sqrt{2601 - 520}}{-} 20$
$x = - \frac{51 \pm \sqrt{2081}}{20}$
Because the number under the square root sign is positive, there are no imaginary roots, only real ones.
$x \approx - \frac{51 \pm 45.62}{20}$
$x \approx - 4.83$ or $x \approx - 0.27$