Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

x\times 3x=2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4,4x.
x^{2}\times 3=2x
Multiply x and x to get x^{2}.
x^{2}\times 3-2x=0
Subtract 2x from both sides.
x\left(3x-2\right)=0
Factor out x.
x=0 x=\frac{2}{3}
To find equation solutions, solve x=0 and 3x-2=0.
x=\frac{2}{3}
Variable x cannot be equal to 0.
x\times 3x=2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4,4x.
x^{2}\times 3=2x
Multiply x and x to get x^{2}.
x^{2}\times 3-2x=0
Subtract 2x from both sides.
3x^{2}-2x=0
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(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±2}{2\times 3}
Take the square root of \left(-2\right)^{2}.
x=\frac{2±2}{2\times 3}
The opposite of -2 is 2.
x=\frac{2±2}{6}
Multiply 2 times 3.
x=\frac{4}{6}
Now solve the equation x=\frac{2±2}{6} when ± is plus. Add 2 to 2.
x=\frac{2}{3}
Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.
x=\frac{0}{6}
Now solve the equation x=\frac{2±2}{6} when ± is minus. Subtract 2 from 2.
x=0
Divide 0 by 6.
x=\frac{2}{3} x=0
The equation is now solved.
x=\frac{2}{3}
Variable x cannot be equal to 0.
x\times 3x=2x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4,4x.
x^{2}\times 3=2x
Multiply x and x to get x^{2}.
x^{2}\times 3-2x=0
Subtract 2x from both sides.
3x^{2}-2x=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{3x^{2}-2x}{3}=\frac{0}{3}
Divide both sides by 3.
x^{2}-\frac{2}{3}x=\frac{0}{3}
Dividing by 3 undoes the multiplication by 3.
x^{2}-\frac{2}{3}x=0
Divide 0 by 3.
x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=\left(-\frac{1}{3}\right)^{2}
Divide -\frac{2}{3}, the coefficient of the x term, by 2 to get -\frac{1}{3}. Then add the square of -\frac{1}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{1}{9}
Square -\frac{1}{3} by squaring both the numerator and the denominator of the fraction.
\left(x-\frac{1}{3}\right)^{2}=\frac{1}{9}
Factor x^{2}-\frac{2}{3}x+\frac{1}{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{1}{3}\right)^{2}}=\sqrt{\frac{1}{9}}
Take the square root of both sides of the equation.
x-\frac{1}{3}=\frac{1}{3} x-\frac{1}{3}=-\frac{1}{3}
Simplify.
x=\frac{2}{3} x=0
Add \frac{1}{3} to both sides of the equation.
x=\frac{2}{3}
Variable x cannot be equal to 0.