# How do you solve the following by quadratic equation for #x# given #15x^2-16xy-15x^2=0#?

##### 2 Answers

(...but see below)

#### Explanation:

Since

A quadratic equation is normally of the form:

We *could* treat the given equation as if it were in this form with

The Quadratic *Formula* tells us

This would give us

This is more of a case of providing information rather than solving the question. Unfortunately the image quality is not so good.

Using Maple I built the following:

#### Explanation:

In this image you can see the contour plot of that intersection.

Consider the cross section of the curved surface in the zy-plane. Observe that the vertex of that quadratic curve is considerably to the left of y=0.

Thus the termination point of the curves LHS has a significantly greater value for z than the RHS. Because of this, in the xy-plane view, the centre line of the saddle is sloping from the bottom left to the top right.

Consequently will influence the contour (implicitplot) of the line z=0 and produce the skewed affect.

In this image you can see the intersection of the plane

Also displayed is the Maple solution for

i.e.

Maples solution reads:

To demonstrate the solution output comparison to the contour plot have a look at:

This compares very well. Note that the saddle surface and the