Question

5w^2-6w+8 (Quadratic Formula)

Answer 1

$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
The given equation is of the form \(ax + bx + c\). Plug in the values:
$$\frac{-(-6) \pm \sqrt{(-6)^2 - 4(5)(8)}}{2(10)}$$

Answer 2

can you explain this a little more better because I don't get it @bloopman

Answer 3

OK, so every quadratic equation is in the following form: \(ax + bx + c = 0\). The equation you posted is actually no different, except \(w = x\). So from herein I shall refer to x as w. We can use the quadratic formula to solve for w:
$$w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Alright, so now we can extract the variables from the equation. Note that all we are doing is taking an equation and inputting values.
$$a = 5, b = -6, c = 8$$
Thus, we just go back in the quadratic equation above and substitute all of the values.
$$w = \frac{6 \pm \sqrt{-6^2 - 4(5)(8)}}{2(5)}$$
Now, let's evaluate this:
$$w = \frac{6 \pm \sqrt{36 - 160}}{2(5)}$$
It has complex roots.
$$w = \frac{6 \pm 2i\sqrt{31}}{10}$$