Solve for x
x=1
x=-1
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3x^{2}+\frac{4}{2}=5
Multiply x and x to get x^{2}.
3x^{2}+2=5
Divide 4 by 2 to get 2.
3x^{2}=5-2
Subtract 2 from both sides.
3x^{2}=3
Subtract 2 from 5 to get 3.
x^{2}=\frac{3}{3}
Divide both sides by 3.
x^{2}=1
Divide 3 by 3 to get 1.
x=1 x=-1
Take the square root of both sides of the equation.
3x^{2}+\frac{4}{2}=5
Multiply x and x to get x^{2}.
3x^{2}+2=5
Divide 4 by 2 to get 2.
3x^{2}+2-5=0
Subtract 5 from both sides.
3x^{2}-3=0
Subtract 5 from 2 to get -3.
x=\frac{0±\sqrt{0^{2}-4\times 3\left(-3\right)}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\left(-3\right)}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\left(-3\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{36}}{2\times 3}
Multiply -12 times -3.
x=\frac{0±6}{2\times 3}
Take the square root of 36.
x=\frac{0±6}{6}
Multiply 2 times 3.
x=1
Now solve the equation x=\frac{0±6}{6} when ± is plus. Divide 6 by 6.
x=-1
Now solve the equation x=\frac{0±6}{6} when ± is minus. Divide -6 by 6.
x=1 x=-1
The equation is now solved.
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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}