Solve for c (complex solution)

\left\{\begin{matrix}c=\frac{\Delta }{2}-\frac{55b}{2x}\text{, }&x\neq 0\\c\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.

${c=2Δ −2x55b ,c∈C, x =0b=0andx=0 $

Solve for x (complex solution)

\left\{\begin{matrix}x=\frac{55b}{\Delta -2c}\text{, }&\Delta \neq 2c\\x\in \mathrm{C}\text{, }&b=0\text{ and }\Delta =2c\end{matrix}\right.

${x=Δ−2c55b ,x∈C, Δ =2cb=0andΔ=2c $

Solve for Δ (complex solution)

\left\{\begin{matrix}\Delta =2c+\frac{55b}{x}\text{, }&x\neq 0\\\Delta \in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.

${Δ=2c+x55b ,Δ∈C, x =0b=0andx=0 $

Solve for b

b=\frac{x\left(\Delta -2c\right)}{55}

$b=55x(Δ−2c) $

Solve for c

\left\{\begin{matrix}c=\frac{\Delta }{2}-\frac{55b}{2x}\text{, }&x\neq 0\\c\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.

${c=2Δ −2x55b ,c∈R, x =0b=0andx=0 $

Solve for x

\left\{\begin{matrix}x=\frac{55b}{\Delta -2c}\text{, }&\Delta \neq 2c\\x\in \mathrm{R}\text{, }&b=0\text{ and }\Delta =2c\end{matrix}\right.

${x=Δ−2c55b ,x∈R, Δ =2cb=0andΔ=2c $

Solve for Δ

\left\{\begin{matrix}\Delta =2c+\frac{55b}{x}\text{, }&x\neq 0\\\Delta \in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.

${Δ=2c+x55b ,Δ∈R, x =0b=0andx=0 $

Graph

Graph Both Sides in 2D

Graph in 2D

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55b+2cx=\Delta x

Swap sides so that all variable terms are on the left hand side.

2cx=\Delta x-55b

Subtract 55b from both sides.

2xc=x\Delta -55b

The equation is in standard form.

\frac{2xc}{2x}=\frac{x\Delta -55b}{2x}

Divide both sides by 2x.

c=\frac{x\Delta -55b}{2x}

Dividing by 2x undoes the multiplication by 2x.

c=\frac{\Delta }{2}-\frac{55b}{2x}

Divide \Delta x-55b by 2x.

\Delta x-2cx=55b

Subtract 2cx from both sides.

\left(\Delta -2c\right)x=55b

Combine all terms containing x.

\frac{\left(\Delta -2c\right)x}{\Delta -2c}=\frac{55b}{\Delta -2c}

Divide both sides by \Delta -2c.

x=\frac{55b}{\Delta -2c}

Dividing by \Delta -2c undoes the multiplication by \Delta -2c.

x\Delta =2cx+55b

The equation is in standard form.

\frac{x\Delta }{x}=\frac{2cx+55b}{x}

Divide both sides by x.

\Delta =\frac{2cx+55b}{x}

Dividing by x undoes the multiplication by x.

\Delta =2c+\frac{55b}{x}

Divide 55b+2cx by x.

55b+2cx=\Delta x

Swap sides so that all variable terms are on the left hand side.

55b=\Delta x-2cx

Subtract 2cx from both sides.

55b=x\Delta -2cx

The equation is in standard form.

\frac{55b}{55}=\frac{x\left(\Delta -2c\right)}{55}

Divide both sides by 55.

b=\frac{x\left(\Delta -2c\right)}{55}

Dividing by 55 undoes the multiplication by 55.

55b+2cx=\Delta x

Swap sides so that all variable terms are on the left hand side.

2cx=\Delta x-55b

Subtract 55b from both sides.

2xc=x\Delta -55b

The equation is in standard form.

\frac{2xc}{2x}=\frac{x\Delta -55b}{2x}

Divide both sides by 2x.

c=\frac{x\Delta -55b}{2x}

Dividing by 2x undoes the multiplication by 2x.

c=\frac{\Delta }{2}-\frac{55b}{2x}

Divide \Delta x-55b by 2x.

\Delta x-2cx=55b

Subtract 2cx from both sides.

\left(\Delta -2c\right)x=55b

Combine all terms containing x.

\frac{\left(\Delta -2c\right)x}{\Delta -2c}=\frac{55b}{\Delta -2c}

Divide both sides by \Delta -2c.

x=\frac{55b}{\Delta -2c}

Dividing by \Delta -2c undoes the multiplication by \Delta -2c.

x\Delta =2cx+55b

The equation is in standard form.

\frac{x\Delta }{x}=\frac{2cx+55b}{x}

Divide both sides by x.

\Delta =\frac{2cx+55b}{x}

Dividing by x undoes the multiplication by x.

\Delta =2c+\frac{55b}{x}

Divide 55b+2cx by x.

Examples

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{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

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4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

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699 * 533

$699∗533$

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]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

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$x→−3lim x_{2}+2x−3x_{2}−9 $