Question

How do you solve `-15x^2 - 10x + 40 = 0` using the quadratic formula?

Answer 1

`x_(1,2) = -(1 +-5)/3`

Explanation:

For a general form quadratic equation

`color(blue)(ax^2 + bx + c = 0)`

the two possible roots of the equation take the form - this is the quadratic formula

`color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)`

Now, your quadratic equation looks like this

`-15x^2 - 10x + 40 = 0`

You can divide all the terms by `5` to simplify it

`-3x^2 - 2x + 8 = 0`

In your case, you have `a=-3`, `b=-2`, and `c=8`. THis means that the two solutions will be

`x_(1,2) = (-(-2) +- sqrt( (-2)^2 - 4 * (-3) * 8))/(2 * (-3))`

`x_(1,2) = (2 +- sqrt(100))/(-6)`

`x_(1,2) = (2 +- 10)/(-6) = -(1 +- 5)/3 = {(x_1 = (-1 - 5)/3 = -2), (x_2 = (-1 + 5)/3 = 4/3) :}`

Your quadratic equation will thus have two roots, `x_1 = color(green)(-2)` and `x_2 = color(green)(4/3)`.