Solve for α
\alpha =12\beta ^{2}
\beta \neq 0
Solve for β
\beta =\frac{\sqrt{3\alpha }}{6}
\beta =-\frac{\sqrt{3\alpha }}{6}\text{, }\alpha >0
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3\alpha =6\beta \times 6\beta
Multiply both sides of the equation by 6\beta .
3\alpha =6\beta ^{2}\times 6
Multiply \beta and \beta to get \beta ^{2}.
3\alpha =36\beta ^{2}
Multiply 6 and 6 to get 36.
\frac{3\alpha }{3}=\frac{36\beta ^{2}}{3}
Divide both sides by 3.
\alpha =\frac{36\beta ^{2}}{3}
Dividing by 3 undoes the multiplication by 3.
\alpha =12\beta ^{2}
Divide 36\beta ^{2} by 3.
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