What are the solutions to the equation 4y^2+8y-12y-7=0 ?

The solutions to the equation 4y^2+8y-12y-7=0 are y=(1+2sqrt(2))/2 ,y=(1-2sqrt(2))/2

Find the zeros of 4y^2+8y-12y-7=0

The zeros of 4y^2+8y-12y-7=0 are y=(1+2sqrt(2))/2 ,y=(1-2sqrt(2))/2

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4 y^{2} + 8 y - 12 y - 7 = 0

y = \frac{1 + 2 2}{2}, y = \frac{1 - 2 2}{2}

Decimal Notation

y = 1.91421 \dots, y = - 0.91421 \dots

Solution steps

4 y^{2} + 8 y - 12 y - 7 = 0

Refine

4 y^{2} - 4 y - 7 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 4 (- 7) = 82

y_{1, 2} = \frac{- ( - 4 ) \pm 8 2}{2 \cdot 4}

Separate the solutions

y_{1} = \frac{- ( - 4 ) + 8 2}{2 \cdot 4}, y_{2} = \frac{- ( - 4 ) - 8 2}{2 \cdot 4}

y = \frac{- ( - 4 ) + 8 2}{2 \cdot 4} : \frac{1 + 2 2}{2}

y = \frac{- ( - 4 ) - 8 2}{2 \cdot 4} : \frac{1 - 2 2}{2}

The solutions to the quadratic equation are:

y = \frac{1 + 2 2}{2}, y = \frac{1 - 2 2}{2}

6 x^{2} + 4 x + 5 = 0

y, x = y^{2} - 4 y

x (x - 2) = x (3 x - 1)

6 x^{2} - 17 x - 3 = 0

x^{2} - 10 x + 29

What are the solutions to the equation 4y^2+8y-12y-7=0 ?
The solutions to the equation 4y^2+8y-12y-7=0 are y=(1+2sqrt(2))/2 ,y=(1-2sqrt(2))/2
Find the zeros of 4y^2+8y-12y-7=0
The zeros of 4y^2+8y-12y-7=0 are y=(1+2sqrt(2))/2 ,y=(1-2sqrt(2))/2