Thread: Qudratic equation for bending point

I have completed an assignment but for this 1 question, any help would be appreciated

In construction it is important to be aware of weak points in a beam to ensure they can hold the maximum possible weight
The bending moment M at a point in a beam is given by the formula below

3x(20-x)
M = _______

2

Where x metres is the distance from the point of support. Calculate the value of x when the bending moment is Nm. A trial and error method will not be accepted.

If the bending moment is then we have:



Multiply through by 2, then distribute on the right:



Arrange quadratic in standard form:



Now, apply the quadratic formula to find x.