A bus travels 300 km from Tema to Takoradi at a speed of (x+10) km/h and returns from Takoradi to Tema at a speed of (x-10) km/h. If the total journey took 8 hours, find the value of x.

Let $D$ be the distance, $S$ be the speed, and $T$ be the time. The relationship is $T = \frac{D}{S}$.
The distance for each leg of the journey is $D = 300$ km.
The speed from Tema to Takoradi is $S_1 = (x+10)$ km/h.
The speed from Takoradi to Tema (return) is $S_2 = (x-10)$ km/h.
The total time for the round trip is $T_{total} = 8$ hours.

Time taken to travel from Tema to Takoradi ($T_1$):

Time taken to travel from Takoradi to Tema ($T_2$):

The total time is the sum of the times for each leg:

Multiply the entire equation by the common denominator $(x+10)(x-10)$ to eliminate the fractions:

Expand the terms:

Rearrange the equation into a standard quadratic form $ax^2 + bx + c = 0$:

Divide the entire equation by 8 to simplify:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
For $x^2 - 75x - 100 = 0$, we have $a=1$, $b=-75$, and $c=-100$.

Since $\sqrt{6025} \approx 77.62$, we have:

Speed cannot be negative. If $x = -1.31$, then $x-10 = -1.31-10 = -11.31$, which is a negative speed. Therefore, $x_2$ is not a valid solution.
The valid value for $x$ is $x_1$.

The value of $x$ is $\boxed{\frac{75 + \sqrt{6025}}{2}}$.