Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$2x+ \frac{ 3 }{ x } =5 \frac{ 1 }{ 2 }$$

Answer

x=(5+sqrt(71)*IM)/8,(5-sqrt(71)*IM)/8

Solution


Simplify  \(5\times \frac{1}{2}\)  to  \(\frac{5}{2}\).
\[2x+\frac{3}{x}=\frac{5}{2}\]
Multiply both sides by \(2x\).
\[4{x}^{2}+6=5x\]
Move all terms to one side.
\[4{x}^{2}+6-5x=0\]
Use the Quadratic Formula.
\[x=\frac{5+\sqrt{71}\imath }{8},\frac{5-\sqrt{71}\imath }{8}\]
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