$$\sqrt{\frac{x}{-4.9}} - \frac{x}{340} = 4.68$$
The following is my work so far:
$$\sqrt{\frac{x}{-4.9}} = 4.68 + \frac{x}{340}$$ $$\frac{x}{-4.9} = 21.9 + \frac{x^2}{115600} + \frac{3182.4x}{115600}$$ $$x^2 + 26774.2x + 2531640 = 0$$
Using the quadratic formula, I get
$$x_1 = -94.9$$ $$x_2 = -26679.3$$
However, the answer in my book only mentions $-94.9$. I checked a couple of online equation solvers; also they only mention $-94.9$. Additionally, plugging in $-26679.3$ into the original equation does not work - however plugging it into the derived quadratic does. This must mean my derived quadratic equation is incorrect - does anyone have any idea why?
It's because when you squared both sides of your equation, you made the "negative square root" into a possible solution, whereas $\sqrt{}$ always means the positive square root.