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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.

Re: Qudratic equation for bending point

If the bending moment is $\displaystyle Nm$ then we have:

$\displaystyle Nm=\frac{3x(20-x)}{2}$

Multiply through by 2, then distribute on the right:

$\displaystyle 2Nm=60x-3x^2$

Arrange quadratic in standard form:

$\displaystyle 3x^2-60x+2Nm=0$

Now, apply the quadratic formula to find *x*.