What are the solutions to the equation 2y(y-5)=3(2y-1)-4 ?

The solutions to the equation 2y(y-5)=3(2y-1)-4 are y=(8+5sqrt(2))/2 ,y=(8-5sqrt(2))/2

Find the zeros of 2y(y-5)=3(2y-1)-4

The zeros of 2y(y-5)=3(2y-1)-4 are y=(8+5sqrt(2))/2 ,y=(8-5sqrt(2))/2

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2 y (y - 5) = 3 (2 y - 1) - 4

y = \frac{8 + 5 2}{2}, y = \frac{8 - 5 2}{2}

Decimal

y = 7.53553 \dots, y = 0.46446 \dots

Solution steps

2 y (y - 5) = 3 (2 y - 1) - 4

Expand

2 y (y - 5) : 2 y^{2} - 10 y

Expand

3 (2 y - 1) - 4 : 6 y - 7

2 y^{2} - 10 y = 6 y - 7

Move

7

to the left side

2 y^{2} - 10 y + 7 = 6 y

Move

6 y

to the left side

2 y^{2} - 16 y + 7 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 \cdot 2 \cdot 7}{2 \cdot 2}

(- 16)^{2} - 4 \cdot 2 \cdot 7 = 102

y_{1, 2} = \frac{- ( - 16 ) \pm 10 2}{2 \cdot 2}

Separate the solutions

y_{1} = \frac{- ( - 16 ) + 10 2}{2 \cdot 2}, y_{2} = \frac{- ( - 16 ) - 10 2}{2 \cdot 2}

y = \frac{- ( - 16 ) + 10 2}{2 \cdot 2} : \frac{8 + 5 2}{2}

y = \frac{- ( - 16 ) - 10 2}{2 \cdot 2} : \frac{8 - 5 2}{2}

The solutions to the quadratic equation are:

y = \frac{8 + 5 2}{2}, y = \frac{8 - 5 2}{2}

x^{2} - 12 x - 63 = 9

(- 9 + A x)^{2} = 16 x^{2} + 72 x - 81

6 m^{2} - m - 1 = 0

36 x^{2} = 64

3 x (x - 2) = (x - 2) (x - 6)

What are the solutions to the equation 2y(y-5)=3(2y-1)-4 ?
The solutions to the equation 2y(y-5)=3(2y-1)-4 are y=(8+5sqrt(2))/2 ,y=(8-5sqrt(2))/2
Find the zeros of 2y(y-5)=3(2y-1)-4
The zeros of 2y(y-5)=3(2y-1)-4 are y=(8+5sqrt(2))/2 ,y=(8-5sqrt(2))/2