4. Solve the quadratic equation $2 x^{2}+x-300=0$ using factorisation.

Step 1 ：The quadratic equation is in the form of \(ax^2 + bx + c = 0\). The first step to solve this equation is to factorise it. The factorisation of a quadratic equation involves finding two numbers that add up to the coefficient of x (b) and multiply to the constant term (c). However, in this case, it's not easy to directly factorise the equation because the numbers are large. So, we can use the quadratic formula to solve the equation. The quadratic formula is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 2 ：Substitute the values of a, b, and c into the quadratic formula. Here, a = 2, b = 1, and c = -300.

Step 3 ：Solve the equation to find the solutions. The solutions to the quadratic equation are -12.5 and 12.0. These are the values of x that satisfy the equation.

Step 4 ：Final Answer: The solutions to the quadratic equation \(2 x^{2}+x-300=0\) are \(\boxed{-12.5}\) and \(\boxed{12.0}\).