What is the answer to (6x^2+18x)/(2x^3)= 5/x ?

The answer to (6x^2+18x)/(2x^3)= 5/x is x= 9/2

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(6x^2+18x)/(2x^3)= 5/x

\frac{6 x ^{2} + 18 x}{2 x ^{3}} = \frac{5}{x}

x = \frac{9}{2}

Decimal Notation

x = 4.5

Solution steps

\frac{6 x ^{2} + 18 x}{2 x ^{3}} = \frac{5}{x}

Cross multiply

3 (x + 3) x = x^{2} \cdot 5

Solve

3 (x + 3) x = x^{2} \cdot 5 : x = 0, x = \frac{9}{2}

x = 0, x = \frac{9}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Since the equation is undefined for:

0

x = \frac{9}{2}

2 x - 2 x^{- 2} = 0

\frac{1}{x} - 6 = - 5 x

300000 x - \frac{1505000}{x ^{2}} = 0

\frac{1}{3 x} + \frac{4 x}{6} = 1

\frac{x ^{2}}{x - 1} = 0

What is the answer to (6x^2+18x)/(2x^3)= 5/x ?
The answer to (6x^2+18x)/(2x^3)= 5/x is x= 9/2
Solve for x: (6x^2+18x)/(2x^3)= 5/x
The solution is x= 9/2