Question

What are the solution(s) of `5 - 10x - 3x^2 = 0`?

Answer 1

`x_(1,2) = -5/3 ∓ 2/3sqrt(10)`

Explanation:

For a general form quadratic equation

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

you can find its roots by using the quadratic formula

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

The quadratic equation you were given looks like this

`5 - 10x - 3x^2 = 0`

Rearrange it to match the general form

`-3x^2 - 10x + 5 = 0`

In your case, you have `a = -3`, `b = -10`, and `c = 5`. This means that the two roots will take the form

`x_(1,2) = (-(-10) +- sqrt((-10)^2 - 4 * (-3) * (5)))/(2 * (-3))`

`x_(1,2) = (10 +- sqrt(100 + 60))/((-6))`

`x_(1,2) = (10 +- sqrt(160))/((-6)) = -5/3 ∓ 2/3sqrt(10)`

The two solutions will thus be

`x_1 = -5/3 - 2/3sqrt(10)" "` and `" "x_2 = -5/3 + 2/3sqrt(10)`