What are the solutions to the equation 3/2 y^2-6y= 3/4 y-9 ?

The solutions to the equation 3/2 y^2-6y= 3/4 y-9 are y= 9/4+i(sqrt(15))/4 ,y= 9/4-i(sqrt(15))/4

Find the zeros of 3/2 y^2-6y= 3/4 y-9

The zeros of 3/2 y^2-6y= 3/4 y-9 are y= 9/4+i(sqrt(15))/4 ,y= 9/4-i(sqrt(15))/4

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\frac{3}{2} y^{2} - 6 y = \frac{3}{4} y - 9

y = \frac{9}{4} + i \frac{15}{4}, y = \frac{9}{4} - i \frac{15}{4}

Solution steps

\frac{3}{2} y^{2} - 6 y = \frac{3}{4} y - 9

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

\frac{3}{2} y^{2} \cdot 4 - 6 y \cdot 4 = \frac{3}{4} y \cdot 4 - 9 \cdot 4

Simplify

6 y^{2} - 24 y = 3 y - 36

Move

36

to the left side

6 y^{2} - 24 y + 36 = 3 y

Move

3 y

to the left side

6 y^{2} - 27 y + 36 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 27 ) \pm ( - 27 ) ^{2} - 4 \cdot 6 \cdot 36}{2 \cdot 6}

Simplify

(- 27)^{2} - 4 \cdot 6 \cdot 36 : 315 i

y_{1, 2} = \frac{- ( - 27 ) \pm 3 15 i}{2 \cdot 6}

Separate the solutions

y_{1} = \frac{- ( - 27 ) + 3 15 i}{2 \cdot 6}, y_{2} = \frac{- ( - 27 ) - 3 15 i}{2 \cdot 6}

y = \frac{- ( - 27 ) + 3 15 i}{2 \cdot 6} : \frac{9}{4} + i \frac{15}{4}

y = \frac{- ( - 27 ) - 3 15 i}{2 \cdot 6} : \frac{9}{4} - i \frac{15}{4}

The solutions to the quadratic equation are:

y = \frac{9}{4} + i \frac{15}{4}, y = \frac{9}{4} - i \frac{15}{4}

36 = x^{2} + x^{2}

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

\frac{w ^{2}}{6} - \frac{w}{3} - 4 = 0

x^{2} + 8 x - 49 = - 4

3 (4 x + 3)^{2} + 1 = 16

What are the solutions to the equation 3/2 y^2-6y= 3/4 y-9 ?
The solutions to the equation 3/2 y^2-6y= 3/4 y-9 are y= 9/4+i(sqrt(15))/4 ,y= 9/4-i(sqrt(15))/4
Find the zeros of 3/2 y^2-6y= 3/4 y-9
The zeros of 3/2 y^2-6y= 3/4 y-9 are y= 9/4+i(sqrt(15))/4 ,y= 9/4-i(sqrt(15))/4