Solve 20x^2-39x

$$20 x ^ { 2 } - 39 x$$

Factor

$$x\left(20x-39\right)$$

Solution Steps

Factor out x.

$$x\left(20x-39\right)$$

Steps Using the Quadratic Formula

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.

$$20x^{2}-39x=0$$

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.

$$x=\frac{-\left(-39\right)±\sqrt{\left(-39\right)^{2}}}{2\times 20}$$

Take the square root of \left(-39\right)^{2}.

$$x=\frac{-\left(-39\right)±39}{2\times 20}$$

The opposite of -39 is 39.

$$x=\frac{39±39}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{39±39}{40}$$

Now solve the equation x=\frac{39±39}{40} when ± is plus. Add 39 to 39.

$$x=\frac{78}{40}$$

Reduce the fraction \frac{78}{40} to lowest terms by extracting and canceling out 2.

$$x=\frac{39}{20}$$

Now solve the equation x=\frac{39±39}{40} when ± is minus. Subtract 39 from 39.

$$x=\frac{0}{40}$$

Divide 0 by 40.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{39}{20} for x_{1} and 0 for x_{2}.

$$20x^{2}-39x=20\left(x-\frac{39}{20}\right)x$$

Subtract \frac{39}{20} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$20x^{2}-39x=20\times \frac{20x-39}{20}x$$

Cancel out 20, the greatest common factor in 20 and 20.

$$20x^{2}-39x=\left(20x-39\right)x$$

Evaluate

$$x\left(20x-39\right)$$