Solve for a
a=\frac{\sqrt{3}x}{2}
x\neq 0
Solve for x
x=\frac{2\sqrt{3}a}{3}
a\neq 0
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3x=2a\sqrt{3}
Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6a, the least common multiple of 2a,3.
2a\sqrt{3}=3x
Swap sides so that all variable terms are on the left hand side.
2\sqrt{3}a=3x
The equation is in standard form.
\frac{2\sqrt{3}a}{2\sqrt{3}}=\frac{3x}{2\sqrt{3}}
Divide both sides by 2\sqrt{3}.
a=\frac{3x}{2\sqrt{3}}
Dividing by 2\sqrt{3} undoes the multiplication by 2\sqrt{3}.
a=\frac{\sqrt{3}x}{2}
Divide 3x by 2\sqrt{3}.
a=\frac{\sqrt{3}x}{2}\text{, }a\neq 0
Variable a cannot be equal to 0.
3x=2a\sqrt{3}
Multiply both sides of the equation by 6a, the least common multiple of 2a,3.
3x=2\sqrt{3}a
Reorder the terms.
\frac{3x}{3}=\frac{2\sqrt{3}a}{3}
Divide both sides by 3.
x=\frac{2\sqrt{3}a}{3}
Dividing by 3 undoes the multiplication by 3.
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