Remove parentheses.
\[x+2-\frac{1}{x+2}=\frac{6}{5}\]
Multiply both sides by \(5(x+2)\).
\[5x(x+2)+10(x+2)-5=6(x+2)\]
Simplify.
\[5{x}^{2}+20x+15=6x+12\]
Move all terms to one side.
\[5{x}^{2}+20x+15-6x-12=0\]
Simplify \(5{x}^{2}+20x+15-6x-12\) to \(5{x}^{2}+14x+3\).
\[5{x}^{2}+14x+3=0\]
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, \(a=5\), \(b=14\) and \(c=3\).
\[{x}^{}=\frac{-14+\sqrt{{14}^{2}-4\times 5\times 3}}{2\times 5},\frac{-14-\sqrt{{14}^{2}-4\times 5\times 3}}{2\times 5}\]
Simplify.
\[x=\frac{-14+2\sqrt{34}}{10},\frac{-14-2\sqrt{34}}{10}\]
\[x=\frac{-14+2\sqrt{34}}{10},\frac{-14-2\sqrt{34}}{10}\]
Simplify solutions.
\[x=-\frac{7-\sqrt{34}}{5},-\frac{7+\sqrt{34}}{5}\]
Decimal Form: -0.233810, -2.566190
x=-(7-sqrt(34))/5,-(7+sqrt(34))/5
