How do I solve this problem without a given equation?

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Do I need an equation to figure out $x_2$ and $x_3$ values? Can the equation be obtained from the graph? Much thanks! enter image description here

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If you draw the tangent to the curve at $x_1=6$, it looks like it will intersect the $x$ axis at $x_2=8$. Drawing the tangent at $x_2=8$ will intersect the $x$-axis at $x_3=7$