What are the solutions to the equation solvefor p,(5x^2-2p^2)/x = p/3 ?

The solutions to the equation solvefor p,(5x^2-2p^2)/x = p/3 are p=-(5x)/3 ,p=(3x)/2

Find the zeros of solvefor p,(5x^2-2p^2)/x = p/3

The zeros of solvefor p,(5x^2-2p^2)/x = p/3 are p=-(5x)/3 ,p=(3x)/2

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solve for

p, \frac{5 x ^{2} - 2 p ^{2}}{x} = \frac{p}{3}

p = - \frac{5 x}{3}, p = \frac{3 x}{2}

Solution steps

\frac{5 x ^{2} - 2 p ^{2}}{x} = \frac{p}{3}

Find Least Common Multiplier of

x, 3 : 3 x

Multiply by LCM=

3 x

\frac{5 x ^{2} - 2 p ^{2}}{x} \cdot 3 x = \frac{p}{3} \cdot 3 x; x \neq = 0

Simplify

3 (5 x^{2} - 2 p^{2}) = x p; x \neq = 0

Expand

3 (5 x^{2} - 2 p^{2}) : 15 x^{2} - 6 p^{2}

15 x^{2} - 6 p^{2} = x p; x \neq = 0

Move

x p

to the left side

15 x^{2} - 6 p^{2} - x p = 0; x \neq = 0

Write in the standard form

a x^{2} + b x + c = 0

- 6 p^{2} - x p + 15 x^{2} = 0; x \neq = 0

Solve with the quadratic formula

p_{1, 2} = \frac{- ( - x ) \pm ( - x ) ^{2} - 4 ( - 6 ) \cdot 15 x ^{2}}{2 ( - 6 )}

Simplify

(- x)^{2} - 4 (- 6) \cdot 15 x^{2} : 19 x

p_{1, 2} = \frac{- ( - x ) \pm 19 x}{2 ( - 6 )}

Separate the solutions

p_{1} = \frac{- ( - x ) + 19 x}{2 ( - 6 )}, p_{2} = \frac{- ( - x ) - 19 x}{2 ( - 6 )}

p = \frac{- ( - x ) + 19 x}{2 ( - 6 )} : - \frac{5 x}{3}

p = \frac{- ( - x ) - 19 x}{2 ( - 6 )} : \frac{3 x}{2}

The solutions to the quadratic equation are:

p = - \frac{5 x}{3}, p = \frac{3 x}{2}

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

3 x^{2} + 6 x + d = 0

9 x^{2} = 42 x - 52

5 - 3 (2 x + 1)^{2} = - 22

x^{2} + 5 x = 84

What are the solutions to the equation solvefor p,(5x^2-2p^2)/x = p/3 ?
The solutions to the equation solvefor p,(5x^2-2p^2)/x = p/3 are p=-(5x)/3 ,p=(3x)/2
Find the zeros of solvefor p,(5x^2-2p^2)/x = p/3
The zeros of solvefor p,(5x^2-2p^2)/x = p/3 are p=-(5x)/3 ,p=(3x)/2