Quadratic formula and factoring are leading to different answers

Question

$$x^{ 2 }-2x-15=0$$

By factoring, I get:

$$(x-5)(x+3)$$

Which has the solutions:

$$x=5, x=-3$$

However when I use the quadratic formula (which is what the book saids to use), I get

$$\frac { 2 \pm \sqrt { 4-(4\cdot1\cdot(-15)) } }{ -2 } =$$ $$\frac { 2\pm 8 }{ -2 } $$

Which I evaluate to be $$x=-5, x=3$$

Where am I going wrong?

Answer 1

$$ax^2+bx+c=0\implies x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

$$\implies x^2-2x-15=0\implies x=\frac{2\pm\sqrt{(-2)^2-4\cdot1(-15)}}{2\cdot1}=\frac{2\pm8}2=5,-3$$

Answer 2

Your error is that the denominator should be $2$, not $-2$

Answer 3

The quadratic formula is $$ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} $$ The denominator should be $2$ because \[ a=1 \] \[ b=-2 \] \[ c=-15 \] So then \[ x=\frac{2\pm \sqrt{4-4(-15)}}{2}= \frac{2\pm \sqrt{64}}{2}= \frac{2\pm 8}{2}=1\pm 4 \] Thus $$ x=5 $$ $$ x=-3 $$