Factor
3\left(x-\frac{5-\sqrt{37}}{6}\right)\left(x-\frac{\sqrt{37}+5}{6}\right)
Evaluate
3x^{2}-5x-1
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factor(-5x+3x^{2}-1)
Combine -6x and x to get -5x.
3x^{2}-5x-1=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 3\left(-1\right)}}{2\times 3}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-5\right)±\sqrt{25-4\times 3\left(-1\right)}}{2\times 3}
Square -5.
x=\frac{-\left(-5\right)±\sqrt{25-12\left(-1\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{-\left(-5\right)±\sqrt{25+12}}{2\times 3}
Multiply -12 times -1.
x=\frac{-\left(-5\right)±\sqrt{37}}{2\times 3}
Add 25 to 12.
x=\frac{5±\sqrt{37}}{2\times 3}
The opposite of -5 is 5.
x=\frac{5±\sqrt{37}}{6}
Multiply 2 times 3.
x=\frac{\sqrt{37}+5}{6}
Now solve the equation x=\frac{5±\sqrt{37}}{6} when ± is plus. Add 5 to \sqrt{37}.
x=\frac{5-\sqrt{37}}{6}
Now solve the equation x=\frac{5±\sqrt{37}}{6} when ± is minus. Subtract \sqrt{37} from 5.
3x^{2}-5x-1=3\left(x-\frac{\sqrt{37}+5}{6}\right)\left(x-\frac{5-\sqrt{37}}{6}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5+\sqrt{37}}{6} for x_{1} and \frac{5-\sqrt{37}}{6} for x_{2}.
-5x+3x^{2}-1
Combine -6x and x to get -5x.
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}