# What is the x intercept of yx=6 x^2/2+4x?

What is the x intercept of $yx=6\frac{{x}^{2}}{2}+4x$?
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Willie Smith
The x-intercept is the value(s) of x when y=0

$yx=6\frac{{x}^{2}}{2}+4x$
when y=0 is equivalent to
$3{x}^{2}+4x=0$

This factors as
x(3x+4)=0

with solutions
$x=0\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}x=-\frac{4}{3}$

Alternate way of looking at it
$yx=6{x}^{2}+4x$
can be simplified by dividing by x
provided $x\ne 0$

In this case we would have the linear equation (graph below)
y=3x+4
(with the solution $x=-\frac{4}{3}$ when $x\ne 0$)

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