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3x^{2}-3x=x-1
Use the distributive property to multiply 3x by x-1.
3x^{2}-3x-x=-1
Subtract x from both sides.
3x^{2}-4x=-1
Combine -3x and -x to get -4x.
3x^{2}-4x+1=0
Add 1 to both sides.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 3}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -4 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-4\right)±\sqrt{16-4\times 3}}{2\times 3}
Square -4.
x=\frac{-\left(-4\right)±\sqrt{16-12}}{2\times 3}
Multiply -4 times 3.
x=\frac{-\left(-4\right)±\sqrt{4}}{2\times 3}
Add 16 to -12.
x=\frac{-\left(-4\right)±2}{2\times 3}
Take the square root of 4.
x=\frac{4±2}{2\times 3}
The opposite of -4 is 4.
x=\frac{4±2}{6}
Multiply 2 times 3.
x=\frac{6}{6}
Now solve the equation x=\frac{4±2}{6} when ± is plus. Add 4 to 2.
x=1
Divide 6 by 6.
x=\frac{2}{6}
Now solve the equation x=\frac{4±2}{6} when ± is minus. Subtract 2 from 4.
x=\frac{1}{3}
Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.
x=1 x=\frac{1}{3}
The equation is now solved.
3x^{2}-3x=x-1
Use the distributive property to multiply 3x by x-1.
3x^{2}-3x-x=-1
Subtract x from both sides.
3x^{2}-4x=-1
Combine -3x and -x to get -4x.
\frac{3x^{2}-4x}{3}=-\frac{1}{3}
Divide both sides by 3.
x^{2}-\frac{4}{3}x=-\frac{1}{3}
Dividing by 3 undoes the multiplication by 3.
x^{2}-\frac{4}{3}x+\left(-\frac{2}{3}\right)^{2}=-\frac{1}{3}+\left(-\frac{2}{3}\right)^{2}
Divide -\frac{4}{3}, the coefficient of the x term, by 2 to get -\frac{2}{3}. Then add the square of -\frac{2}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{4}{3}x+\frac{4}{9}=-\frac{1}{3}+\frac{4}{9}
Square -\frac{2}{3} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{1}{9}
Add -\frac{1}{3} to \frac{4}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{2}{3}\right)^{2}=\frac{1}{9}
Factor x^{2}-\frac{4}{3}x+\frac{4}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{1}{9}}
Take the square root of both sides of the equation.
x-\frac{2}{3}=\frac{1}{3} x-\frac{2}{3}=-\frac{1}{3}
Simplify.
x=1 x=\frac{1}{3}
Add \frac{2}{3} to both sides of the equation.