Solve 9/m+3+15=5m

$$\frac { 9 } { m + 3 } + 15 = 5 m$$

Solve for m

$$m = \frac{3 \sqrt{30}}{5} \approx 3.286335345$$

$$m = -\frac{3 \sqrt{30}}{5} \approx -3.286335345$$

Steps by Finding Square Root

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

$$9+\left(m+3\right)\times 15=5m\left(m+3\right)$$

Use the distributive property to multiply m+3 by 15.

$$9+15m+45=5m\left(m+3\right)$$

Add 9 and 45 to get 54.

$$54+15m=5m\left(m+3\right)$$

Use the distributive property to multiply 5m by m+3.

$$54+15m=5m^{2}+15m$$

Subtract 5m^{2} from both sides.

$$54+15m-5m^{2}=15m$$

Subtract 15m from both sides.

$$54+15m-5m^{2}-15m=0$$

Combine 15m and -15m to get 0.

$$54-5m^{2}=0$$

Subtract 54 from both sides. Anything subtracted from zero gives its negation.

$$-5m^{2}=-54$$

Divide both sides by -5.

$$m^{2}=\frac{-54}{-5}$$

Fraction \frac{-54}{-5} can be simplified to \frac{54}{5} by removing the negative sign from both the numerator and the denominator.

$$m^{2}=\frac{54}{5}$$

Take the square root of both sides of the equation.

$$m=\frac{3\sqrt{30}}{5} m=-\frac{3\sqrt{30}}{5}$$

Steps Using the Quadratic Formula

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

$$9+\left(m+3\right)\times 15=5m\left(m+3\right)$$

Use the distributive property to multiply m+3 by 15.

$$9+15m+45=5m\left(m+3\right)$$

Add 9 and 45 to get 54.

$$54+15m=5m\left(m+3\right)$$

Use the distributive property to multiply 5m by m+3.

$$54+15m=5m^{2}+15m$$

Subtract 5m^{2} from both sides.

$$54+15m-5m^{2}=15m$$

Subtract 15m from both sides.

$$54+15m-5m^{2}-15m=0$$

Combine 15m and -15m to get 0.

$$54-5m^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-5m^{2}+54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 54}}{2\left(-5\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-5\right)\times 54}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$m=\frac{0±\sqrt{20\times 54}}{2\left(-5\right)}$$

Multiply 20 times 54.

$$m=\frac{0±\sqrt{1080}}{2\left(-5\right)}$$

Take the square root of 1080.

$$m=\frac{0±6\sqrt{30}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$m=\frac{0±6\sqrt{30}}{-10}$$

Now solve the equation m=\frac{0±6\sqrt{30}}{-10} when ± is plus.

$$m=-\frac{3\sqrt{30}}{5}$$

Now solve the equation m=\frac{0±6\sqrt{30}}{-10} when ± is minus.

$$m=\frac{3\sqrt{30}}{5}$$

The equation is now solved.

$$m=-\frac{3\sqrt{30}}{5} m=\frac{3\sqrt{30}}{5}$$