Solve 15x^2+3/x+7/x=20/x

$$\frac { 15 x ^ { 2 } + 3 } { x } + \frac { 7 } { x } = \frac { 20 } { x }$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$15x^{2}+3+7=20$$

Add 3 and 7 to get 10.

$$15x^{2}+10=20$$

Subtract 10 from both sides.

$$15x^{2}=20-10$$

Subtract 10 from 20 to get 10.

$$15x^{2}=10$$

Divide both sides by 15.

$$x^{2}=\frac{10}{15}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{2}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$15x^{2}+3+7=20$$

Add 3 and 7 to get 10.

$$15x^{2}+10=20$$

Subtract 20 from both sides.

$$15x^{2}+10-20=0$$

Subtract 20 from 10 to get -10.

$$15x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15\left(-10\right)}}{2\times 15}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15\left(-10\right)}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60\left(-10\right)}}{2\times 15}$$

Multiply -60 times -10.

$$x=\frac{0±\sqrt{600}}{2\times 15}$$

Take the square root of 600.

$$x=\frac{0±10\sqrt{6}}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{0±10\sqrt{6}}{30}$$

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

$$x=\frac{\sqrt{6}}{3}$$

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

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$