Solve for y (complex solution)
y=\frac{x^{2}+x^{\frac{3}{2}}-1}{2x}
x\neq 0
Solve for y
y=\frac{x^{2}+x^{\frac{3}{2}}-1}{2x}
x>0
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-2xy+\sqrt{x^{3}}=1-x^{2}
Subtract x^{2} from both sides.
-2xy=1-x^{2}-\sqrt{x^{3}}
Subtract \sqrt{x^{3}} from both sides.
\left(-2x\right)y=-x^{2}-\sqrt{x^{3}}+1
The equation is in standard form.
\frac{\left(-2x\right)y}{-2x}=\frac{1-x^{\frac{3}{2}}-x^{2}}{-2x}
Divide both sides by -2x.
y=\frac{1-x^{\frac{3}{2}}-x^{2}}{-2x}
Dividing by -2x undoes the multiplication by -2x.
y=\frac{x}{2}+\frac{\sqrt{x}}{2}-\frac{1}{2x}
Divide -x^{2}-x^{\frac{3}{2}}+1 by -2x.
-2xy+\sqrt{x^{3}}=1-x^{2}
Subtract x^{2} from both sides.
-2xy=1-x^{2}-\sqrt{x^{3}}
Subtract \sqrt{x^{3}} from both sides.
\left(-2x\right)y=-x^{2}-\sqrt{x^{3}}+1
The equation is in standard form.
\frac{\left(-2x\right)y}{-2x}=\frac{1-x^{\frac{3}{2}}-x^{2}}{-2x}
Divide both sides by -2x.
y=\frac{1-x^{\frac{3}{2}}-x^{2}}{-2x}
Dividing by -2x undoes the multiplication by -2x.
y=\frac{x}{2}+\frac{\sqrt{x}}{2}-\frac{1}{2x}
Divide -x^{2}-x^{\frac{3}{2}}+1 by -2x.
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