What are the solutions to the equation solvefor y,s(y)=3yy+5 ?

The solutions to the equation solvefor y,s(y)=3yy+5 are y=(s+sqrt(s^2-60))/6 ,y=(s-sqrt(s^2-60))/6

Find the zeros of solvefor y,s(y)=3yy+5

The zeros of solvefor y,s(y)=3yy+5 are y=(s+sqrt(s^2-60))/6 ,y=(s-sqrt(s^2-60))/6

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solve for

y, s (y) = 3 yy + 5

y = \frac{s + s ^{2} - 60}{6}, y = \frac{s - s ^{2} - 60}{6}

Solution steps

s (y) = 3 yy + 5

Expand

3 yy + 5 : 3 y^{2} + 5

ys = 3 y^{2} + 5

Switch sides

3 y^{2} + 5 = ys

Move

ys

to the left side

3 y^{2} + 5 - ys = 0

Write in the standard form

a x^{2} + b x + c = 0

3 y^{2} - sy + 5 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - s ) \pm ( - s ) ^{2} - 4 \cdot 3 \cdot 5}{2 \cdot 3}

Simplify

(- s)^{2} - 4 \cdot 3 \cdot 5 : s^{2} - 60

y_{1, 2} = \frac{- ( - s ) \pm s ^{2} - 60}{2 \cdot 3}

Separate the solutions

y_{1} = \frac{- ( - s ) + s ^{2} - 60}{2 \cdot 3}, y_{2} = \frac{- ( - s ) - s ^{2} - 60}{2 \cdot 3}

y = \frac{- ( - s ) + s ^{2} - 60}{2 \cdot 3} : \frac{s + s ^{2} - 60}{6}

y = \frac{- ( - s ) - s ^{2} - 60}{2 \cdot 3} : \frac{s - s ^{2} - 60}{6}

The solutions to the quadratic equation are:

y = \frac{s + s ^{2} - 60}{6}, y = \frac{s - s ^{2} - 60}{6}

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

20 x^{2} + 4 x = 0

(0 - 2)^{2} - (y - 1)^{2} = 9

0.25 x^{2} - 350 x - 100000 = 0

1 - 3 x - 2 x^{2} = 0

What are the solutions to the equation solvefor y,s(y)=3yy+5 ?
The solutions to the equation solvefor y,s(y)=3yy+5 are y=(s+sqrt(s^2-60))/6 ,y=(s-sqrt(s^2-60))/6
Find the zeros of solvefor y,s(y)=3yy+5
The zeros of solvefor y,s(y)=3yy+5 are y=(s+sqrt(s^2-60))/6 ,y=(s-sqrt(s^2-60))/6