Solve for x
x=\frac{1}{2}=0.5
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5x=\frac{5}{3}x+20\left(\frac{2}{3}x-\frac{1}{4}\right)
Multiply \frac{1}{3} and 5 to get \frac{5}{3}.
5x=\frac{5}{3}x+20\times \frac{2}{3}x+20\left(-\frac{1}{4}\right)
Use the distributive property to multiply 20 by \frac{2}{3}x-\frac{1}{4}.
5x=\frac{5}{3}x+\frac{20\times 2}{3}x+20\left(-\frac{1}{4}\right)
Express 20\times \frac{2}{3} as a single fraction.
5x=\frac{5}{3}x+\frac{40}{3}x+20\left(-\frac{1}{4}\right)
Multiply 20 and 2 to get 40.
5x=\frac{5}{3}x+\frac{40}{3}x+\frac{20\left(-1\right)}{4}
Express 20\left(-\frac{1}{4}\right) as a single fraction.
5x=\frac{5}{3}x+\frac{40}{3}x+\frac{-20}{4}
Multiply 20 and -1 to get -20.
5x=\frac{5}{3}x+\frac{40}{3}x-5
Divide -20 by 4 to get -5.
5x=15x-5
Combine \frac{5}{3}x and \frac{40}{3}x to get 15x.
5x-15x=-5
Subtract 15x from both sides.
-10x=-5
Combine 5x and -15x to get -10x.
x=\frac{-5}{-10}
Divide both sides by -10.
x=\frac{1}{2}
Reduce the fraction \frac{-5}{-10} to lowest terms by extracting and canceling out -5.
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}