Solve 20/w-3=2w

$$\frac { 20 } { w - 3 } = 2 w$$

Solve for w

$$w=-2$$

$$w=5$$

Steps Using the Quadratic Formula

Variable w cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by w-3.

$$20=2w\left(w-3\right)$$

Use the distributive property to multiply 2w by w-3.

$$20=2w^{2}-6w$$

Swap sides so that all variable terms are on the left hand side.

$$2w^{2}-6w=20$$

Subtract 20 from both sides.

$$2w^{2}-6w-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -6 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 2\left(-20\right)}}{2\times 2}$$

Square -6.

$$w=\frac{-\left(-6\right)±\sqrt{36-4\times 2\left(-20\right)}}{2\times 2}$$

Multiply -4 times 2.

$$w=\frac{-\left(-6\right)±\sqrt{36-8\left(-20\right)}}{2\times 2}$$

Multiply -8 times -20.

$$w=\frac{-\left(-6\right)±\sqrt{36+160}}{2\times 2}$$

Add 36 to 160.

$$w=\frac{-\left(-6\right)±\sqrt{196}}{2\times 2}$$

Take the square root of 196.

$$w=\frac{-\left(-6\right)±14}{2\times 2}$$

The opposite of -6 is 6.

$$w=\frac{6±14}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{6±14}{4}$$

Now solve the equation w=\frac{6±14}{4} when ± is plus. Add 6 to 14.

$$w=\frac{20}{4}$$

Divide 20 by 4.

$$w=5$$

Now solve the equation w=\frac{6±14}{4} when ± is minus. Subtract 14 from 6.

$$w=-\frac{8}{4}$$

Divide -8 by 4.

$$w=-2$$

The equation is now solved.

$$w=5 w=-2$$

Steps for Completing the Square

Variable w cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by w-3.

$$20=2w\left(w-3\right)$$

Use the distributive property to multiply 2w by w-3.

$$20=2w^{2}-6w$$

Swap sides so that all variable terms are on the left hand side.

$$2w^{2}-6w=20$$

Divide both sides by 2.

$$\frac{2w^{2}-6w}{2}=\frac{20}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$w^{2}+\left(-\frac{6}{2}\right)w=\frac{20}{2}$$

Divide -6 by 2.

$$w^{2}-3w=\frac{20}{2}$$

Divide 20 by 2.

$$w^{2}-3w=10$$

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-3w+\left(-\frac{3}{2}\right)^{2}=10+\left(-\frac{3}{2}\right)^{2}$$

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$w^{2}-3w+\frac{9}{4}=10+\frac{9}{4}$$

Add 10 to \frac{9}{4}.

$$w^{2}-3w+\frac{9}{4}=\frac{49}{4}$$

Factor w^{2}-3w+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-\frac{3}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-\frac{3}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$w-\frac{3}{2}=\frac{7}{2} w-\frac{3}{2}=-\frac{7}{2}$$

Add \frac{3}{2} to both sides of the equation.

$$w=5 w=-2$$