You can start by rewriting the equation so that the right side equals zero. Add [tex]-7x[/tex] and [tex]8[/tex] to both sides.
[tex]x^2+7x+8=0[/tex]
You can now use the quadratic equation (below), where [tex]a=1, b=7,[/tex] and [tex]c=8[/tex], to find solutions. Plug in these values for [tex]a, b,[/tex] and [tex]c[/tex] into the equation and simplify.
[tex] \frac{-b \pm \sqrt{b^2-4(ac)}} {2a}[/tex]
[tex] \frac{-7 \pm \sqrt{7^2-4(1 \times 8)}} {2 \times 1}[/tex]
[tex] \frac{-7 \pm \sqrt{49-32}} {2}[/tex]
[tex] \frac{-7 \pm \sqrt{17}} {2}[/tex]
The final answer is the combination of both solutions.
[tex]x=\frac{-7}{2} \pm \frac{\sqrt{17}} {2} \approx -3.5 \pm 2.06.[/tex]
Or approximately...
[tex]x=(-3.5-2.06) \approx -5.56, (-3.5+2.06) \approx-1.44[/tex]
