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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.