To solve this equation, we can set it equal to zero and then factor it:

[tex]x^2 + x - 80 = 0[/tex]

Now we can factor the equation using the roots of the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

In this case, a = 1, b = 1, and c = -80. Plugging these values into the formula:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-80)}}{2(1)}[/tex]

[tex]x = \frac{-1 \pm \sqrt{1 + 320}}{2}[/tex]

[tex]x = \frac{-1 \pm \sqrt{321}}{2}[/tex]

So the solutions to the equation are:

[tex]x = \frac{-1 + \sqrt{321}}{2}[/tex] and [tex]x = \frac{-1 - \sqrt{321}}{2}[/tex]