What are the solutions to the equation 4y=7y(y-1)-3(y-1) ?

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

Find the zeros of 4y=7y(y-1)-3(y-1)

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4 y = 7 y (y - 1) - 3 (y - 1)

y = \frac{7 + 2 7}{7}, y = \frac{7 - 2 7}{7}

Decimal Notation

y = 1.75592 \dots, y = 0.24407 \dots

Solution steps

4 y = 7 y (y - 1) - 3 (y - 1)

Expand

7 y (y - 1) - 3 (y - 1) : 7 y^{2} - 10 y + 3

4 y = 7 y^{2} - 10 y + 3

Switch sides

7 y^{2} - 10 y + 3 = 4 y

Move

4 y

to the left side

7 y^{2} - 14 y + 3 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 7 \cdot 3}{2 \cdot 7}

(- 14)^{2} - 4 \cdot 7 \cdot 3 = 47

y_{1, 2} = \frac{- ( - 14 ) \pm 4 7}{2 \cdot 7}

Separate the solutions

y_{1} = \frac{- ( - 14 ) + 4 7}{2 \cdot 7}, y_{2} = \frac{- ( - 14 ) - 4 7}{2 \cdot 7}

y = \frac{- ( - 14 ) + 4 7}{2 \cdot 7} : \frac{7 + 2 7}{7}

y = \frac{- ( - 14 ) - 4 7}{2 \cdot 7} : \frac{7 - 2 7}{7}

The solutions to the quadratic equation are:

y = \frac{7 + 2 7}{7}, y = \frac{7 - 2 7}{7}

x^{2} - 12 x - 108 = 0

4 = (x + 7)^{2}

k^{2} - k + 1 = 0

3 x^{2} - 7 = 41

0 = 40 + 5 \cdot t - 5 \cdot t^{2}

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