Solve for N
N=\frac{x\left(x-1\right)}{2}
Solve for x (complex solution)
x=\frac{\sqrt{8N+1}+1}{2}
x=\frac{-\sqrt{8N+1}+1}{2}
Solve for x
x=\frac{\sqrt{8N+1}+1}{2}
x=\frac{-\sqrt{8N+1}+1}{2}\text{, }N\geq -\frac{1}{8}
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N=\frac{1}{2}x^{2}-\frac{1}{2}x
Divide each term of x^{2}-x by 2 to get \frac{1}{2}x^{2}-\frac{1}{2}x.
Examples
Quadratic equation
{ 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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}