Solve for x
x=\frac{y^{2}-5}{8}
y\geq 0
Solve for x (complex solution)
x=\frac{y^{2}-5}{8}
arg(y)<\pi \text{ or }y=0
Solve for y
y=\sqrt{8x+5}
x\geq -\frac{5}{8}
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\sqrt{8x+5}=y
Swap sides so that all variable terms are on the left hand side.
8x+5=y^{2}
Square both sides of the equation.
8x+5-5=y^{2}-5
Subtract 5 from both sides of the equation.
8x=y^{2}-5
Subtracting 5 from itself leaves 0.
\frac{8x}{8}=\frac{y^{2}-5}{8}
Divide both sides by 8.
x=\frac{y^{2}-5}{8}
Dividing by 8 undoes the multiplication by 8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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