What are the solutions to the equation solvefor y,(3y^2)/m+m=(7y)/2 ?

The solutions to the equation solvefor y,(3y^2)/m+m=(7y)/2 are y=(2m)/3 ,y= m/2

Find the zeros of solvefor y,(3y^2)/m+m=(7y)/2

The zeros of solvefor y,(3y^2)/m+m=(7y)/2 are y=(2m)/3 ,y= m/2

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y, \frac{3 y ^{2}}{m} + m = \frac{7 y}{2}

y = \frac{2 m}{3}, y = \frac{m}{2}

Solution steps

\frac{3 y ^{2}}{m} + m = \frac{7 y}{2}

Find Least Common Multiplier of

m, 2 : 2 m

Multiply by LCM=

2 m

\frac{3 y ^{2}}{m} \cdot 2 m + m \cdot 2 m = \frac{7 y}{2} \cdot 2 m; m \neq = 0

Simplify

6 y^{2} + 2 m^{2} = 7 m y; m \neq = 0

Move

7 m y

to the left side

6 y^{2} + 2 m^{2} - 7 m y = 0; m \neq = 0

Write in the standard form

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

6 y^{2} - 7 m y + 2 m^{2} = 0; m \neq = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 7 m ) \pm ( - 7 m ) ^{2} - 4 \cdot 6 \cdot 2 m ^{2}}{2 \cdot 6}

Simplify

(- 7 m)^{2} - 4 \cdot 6 \cdot 2 m^{2} : m

y_{1, 2} = \frac{- ( - 7 m ) \pm m}{2 \cdot 6}

Separate the solutions

y_{1} = \frac{- ( - 7 m ) + m}{2 \cdot 6}, y_{2} = \frac{- ( - 7 m ) - m}{2 \cdot 6}

y = \frac{- ( - 7 m ) + m}{2 \cdot 6} : \frac{2 m}{3}

y = \frac{- ( - 7 m ) - m}{2 \cdot 6} : \frac{m}{2}

The solutions to the quadratic equation are:

y = \frac{2 m}{3}, y = \frac{m}{2}

4 x^{2} - 42 x = 7 x - 12

5 x^{2} - 14 x - 3

- 4 x^{2} + x = 0

x^{2} = 3 x + 8

x^{2} + 3.2 \cdot 1 0^{- 5} x - 8 \cdot 1 0^{- 7} = 0

What are the solutions to the equation solvefor y,(3y^2)/m+m=(7y)/2 ?
The solutions to the equation solvefor y,(3y^2)/m+m=(7y)/2 are y=(2m)/3 ,y= m/2
Find the zeros of solvefor y,(3y^2)/m+m=(7y)/2
The zeros of solvefor y,(3y^2)/m+m=(7y)/2 are y=(2m)/3 ,y= m/2