Solve for x
x=\frac{y^{2}-3}{2}
y\geq 0
Solve for x (complex solution)
x=\frac{y^{2}-3}{2}
arg(y)<\pi \text{ or }y=0
Solve for y
y=\sqrt{2x+3}
x\geq -\frac{3}{2}
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\sqrt{2x+3}=y
Swap sides so that all variable terms are on the left hand side.
2x+3=y^{2}
Square both sides of the equation.
2x+3-3=y^{2}-3
Subtract 3 from both sides of the equation.
2x=y^{2}-3
Subtracting 3 from itself leaves 0.
\frac{2x}{2}=\frac{y^{2}-3}{2}
Divide both sides by 2.
x=\frac{y^{2}-3}{2}
Dividing by 2 undoes the multiplication by 2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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