What are the solutions to the equation 4(-2-3y)^2+3y^2=7 ?

The solutions to the equation 4(-2-3y)^2+3y^2=7 are y=-3/13 ,y=-1

Find the zeros of 4(-2-3y)^2+3y^2=7

The zeros of 4(-2-3y)^2+3y^2=7 are y=-3/13 ,y=-1

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4 (- 2 - 3 y)^{2} + 3 y^{2} = 7

y = - \frac{3}{13}, y = - 1

Decimal Notation

y = - 0.23076 \dots, y = - 1

Solution steps

4 (- 2 - 3 y)^{2} + 3 y^{2} = 7

Expand

4 (- 2 - 3 y)^{2} + 3 y^{2} : 16 + 48 y + 39 y^{2}

16 + 48 y + 39 y^{2} = 7

Move

7

to the left side

39 y^{2} + 48 y + 9 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- 48 \pm 4 8 ^{2} - 4 \cdot 39 \cdot 9}{2 \cdot 39}

4 8^{2} - 4 \cdot 39 \cdot 9 = 30

y_{1, 2} = \frac{- 48 \pm 30}{2 \cdot 39}

Separate the solutions

y_{1} = \frac{- 48 + 30}{2 \cdot 39}, y_{2} = \frac{- 48 - 30}{2 \cdot 39}

y = \frac{- 48 + 30}{2 \cdot 39} : - \frac{3}{13}

y = \frac{- 48 - 30}{2 \cdot 39} : - 1

The solutions to the quadratic equation are:

y = - \frac{3}{13}, y = - 1

x^{2} - 3 x + \frac{1}{3} = 0

12 x^{2} - 132 x + 216 = 0

0 = x^{2} + 8 x + 9

x^{2} - x - 6 = 420

x, 9 x^{2} + 4 y^{2} - 9 x - 24 y + 225 = 0

What are the solutions to the equation 4(-2-3y)^2+3y^2=7 ?
The solutions to the equation 4(-2-3y)^2+3y^2=7 are y=-3/13 ,y=-1
Find the zeros of 4(-2-3y)^2+3y^2=7
The zeros of 4(-2-3y)^2+3y^2=7 are y=-3/13 ,y=-1