Multiply both sides by the Least Common Denominator: \(30(x-7)(x+4)\).
\[30(x+4)-30(x-7)=11(x-7)(x+4)\]
Simplify.
\[330=11{x}^{2}-33x-308\]
Move all terms to one side.
\[330-11{x}^{2}+33x+308=0\]
Simplify \(330-11{x}^{2}+33x+308\) to \(638-11{x}^{2}+33x\).
\[638-11{x}^{2}+33x=0\]
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, \(a=-11\), \(b=33\) and \(c=638\).
\[{x}^{}=\frac{-33+\sqrt{{33}^{2}-4\times -11\times 638}}{2\times -11},\frac{-33-\sqrt{{33}^{2}-4\times -11\times 638}}{2\times -11}\]
Simplify.
\[x=\frac{-33+11\sqrt{241}}{-22},\frac{-33-11\sqrt{241}}{-22}\]
\[x=\frac{-33+11\sqrt{241}}{-22},\frac{-33-11\sqrt{241}}{-22}\]
Simplify solutions.
\[x=\frac{3-\sqrt{241}}{2},\frac{3+\sqrt{241}}{2}\]
Decimal Form: -6.262087, 9.262087
x=(3-sqrt(241))/2,(3+sqrt(241))/2
