Factor out the common term \(2\).
\[3-\frac{1}{2x}=\frac{2(3-5x)}{2x+4}-2\]
Factor out the common term \(2\).
\[3-\frac{1}{2x}=\frac{2(3-5x)}{2(x+2)}-2\]
Cancel \(2\).
\[3-\frac{1}{2x}=\frac{3-5x}{x+2}-2\]
Multiply both sides by the Least Common Denominator: \(2x(x+2)\).
\[6x(x+2)-x-2=2x(3-5x)-4x(x+2)\]
Simplify.
\[6{x}^{2}+11x-2=-2x-14{x}^{2}\]
Move all terms to one side.
\[6{x}^{2}+11x-2+2x+14{x}^{2}=0\]
Simplify \(6{x}^{2}+11x-2+2x+14{x}^{2}\) to \(20{x}^{2}+13x-2\).
\[20{x}^{2}+13x-2=0\]
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, \(a=20\), \(b=13\) and \(c=-2\).
\[{x}^{}=\frac{-13+\sqrt{{13}^{2}-4\times 20\times -2}}{2\times 20},\frac{-13-\sqrt{{13}^{2}-4\times 20\times -2}}{2\times 20}\]
Simplify.
\[x=\frac{-13+\sqrt{329}}{40},\frac{-13-\sqrt{329}}{40}\]
\[x=\frac{-13+\sqrt{329}}{40},\frac{-13-\sqrt{329}}{40}\]
Decimal Form: 0.128459, -0.778459
x=(-13+sqrt(329))/40,(-13-sqrt(329))/40
