<s>[INST] Quadratic equation 4 need some guidance with a quadratic equation.
Suppose $x^2+20x-4000=0$
Here is what I have done so far;
Using the Quadratic Equation $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ where from the above equation, $a=1$, $b=20$, $c=-4000$, we find
$$\begin{align*}x&=\frac{-20+\sqrt{(20)^2-(4)(1)(-4000)}}{2\times 1}\\
             &=\frac{-20+\sqrt{16400}}{1}\\
              &=108.0624847 \end{align*}$$
and
$$\begin{align*} x&=\frac{-20-\sqrt{20^2-(4)(1)(-4000)}}{2\times1}\\
             &=\frac{-20-\sqrt{16400}}{1}    \\
              &=-148.0624847 \end{align*}$$
Neither of these values for $x$ prove correct when applied to $x^2+20x-4000=0$.
I know something is wrong but I can’t figure out what. Any guidance would be appreciated.
 [/INST] Did you figure it out?? I think everyone pointed out where you went wrong, but just to be sure:
$x=\frac{-20+\sqrt{20^2-(4)(1) (-4000)}}{2*\ 1}$
$\frac{1}{2} (-20-20 \sqrt{41})$
= $54.03124237$
And similarly 
$x=\frac{-20-\sqrt{20^2-(4)(1) (-4000)}}{2*\ 1}$
=$\frac{1}{2} (-20+20 \sqrt{41})$
$=-74.03124237$
I used Mathematica to check my work:
Letting $answer\text{=}-74.03124237$
$=answer^2+20 answer-4000$
= 0
Similarly, 
$answer\text {=} 54.03124237$
$=answer^2+20 answer-4000$
=0
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