Multiply both sides by the Least Common Denominator: \(2m(m+3)(m-4)\).
\[4422m(m-4)=5(m+3)(m-4)-2m(m+3)\]
Simplify.
\[4422{m}^{2}-17688m=3{m}^{2}-11m-60\]
Move all terms to one side.
\[4422{m}^{2}-17688m-3{m}^{2}+11m+60=0\]
Simplify \(4422{m}^{2}-17688m-3{m}^{2}+11m+60\) to \(4419{m}^{2}-17677m+60\).
\[4419{m}^{2}-17677m+60=0\]
Use the Quadratic Formula.
In general, given \(a{x}^{2}+bx+c=0\), there exists two solutions where:
\[x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}\]
In this case, \(a=4419\), \(b=-17677\) and \(c=60\).
\[{m}^{}=\frac{17677+\sqrt{{(-17677)}^{2}-4\times 4419\times 60}}{2\times 4419},\frac{17677-\sqrt{{(-17677)}^{2}-4\times 4419\times 60}}{2\times 4419}\]
Simplify.
\[m=\frac{17677+\sqrt{{17677}^{2}-1060560}}{8838},\frac{17677-\sqrt{{17677}^{2}-1060560}}{8838}\]
\[m=\frac{17677+\sqrt{{17677}^{2}-1060560}}{8838},\frac{17677-\sqrt{{17677}^{2}-1060560}}{8838}\]
Decimal Form: 3.996829, 0.003397
m=(17677+sqrt(17677^2-1060560))/8838,(17677-sqrt(17677^2-1060560))/8838
