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5x+7=y^{2}
Swap sides so that all variable terms are on the left hand side.
5x=y^{2}-7
Subtract 7 from both sides.
\frac{5x}{5}=\frac{y^{2}-7}{5}
Divide both sides by 5.
x=\frac{y^{2}-7}{5}
Dividing by 5 undoes the multiplication by 5.