Factor out the common term \(x\).
\[\frac{x(x-5)}{8}=\frac{3}{4}\]
Multiply both sides by \(8\).
\[x(x-5)=6\]
Expand.
\[{x}^{2}-5x=6\]
Move all terms to one side.
\[{x}^{2}-5x-6=0\]
Factor \({x}^{2}-5x-6\).
Ask: Which two numbers add up to \(-5\) and multiply to \(-6\)?
Rewrite the expression using the above.
\[(x-6)(x+1)\]
\[(x-6)(x+1)=0\]
Solve for \(x\).
Ask: When will \((x-6)(x+1)\) equal zero?
When \(x-6=0\) or \(x+1=0\)
Solve each of the 2 equations above.
\[x=6,-1\]
\[x=6,-1\]
x=6,-1
