Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\sqrt{5x}+\frac{2x}{\sqrt{3}}=0\]
Separate terms with roots from terms without roots.
\[\sqrt{5x}=-\frac{2x}{\sqrt{3}}\]
Square both sides.
\[5x=\frac{4{x}^{2}}{3}\]
Multiply both sides by \(3\).
\[15x=4{x}^{2}\]
Move all terms to one side.
\[15x-4{x}^{2}=0\]
Factor out the common term \(x\).
\[x(15-4x)=0\]
Solve for \(x\).
Ask: When will \(x(15-4x)\) equal zero?
When \(x=0\) or \(15-4x=0\)
Solve each of the 2 equations above.
\[x=0,\frac{15}{4}\]
\[x=0,\frac{15}{4}\]
Check solution
When \(x=\frac{15}{4}\), the original equation \(\sqrt{5x}+\frac{2}{\sqrt{3}}x=0\) does not hold true.We will drop \(x=\frac{15}{4}\) from the solution set.
