What are the solutions to the equation y=a(4a-5),a=3 ?

The solutions to the equation y=a(4a-5),a=3 are a=(5+sqrt(25+16y))/8 ,a=(5-sqrt(25+16y))/8

Find the zeros of y=a(4a-5),a=3

The zeros of y=a(4a-5),a=3 are a=(5+sqrt(25+16y))/8 ,a=(5-sqrt(25+16y))/8

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y = a (4 a - 5), a = 3

a = \frac{5 + 25 + 16 y}{8}, a = \frac{5 - 25 + 16 y}{8}

Solution steps

y = a (4 a - 5)

Expand

a (4 a - 5) : 4 a^{2} - 5 a

y = 4 a^{2} - 5 a

Switch sides

4 a^{2} - 5 a = y

Move

y

to the left side

4 a^{2} - 5 a - y = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 4 ( - y )}{2 \cdot 4}

Simplify

(- 5)^{2} - 4 \cdot 4 (- y) : 25 + 16 y

a_{1, 2} = \frac{- ( - 5 ) \pm 25 + 16 y}{2 \cdot 4}

Separate the solutions

a_{1} = \frac{- ( - 5 ) + 25 + 16 y}{2 \cdot 4}, a_{2} = \frac{- ( - 5 ) - 25 + 16 y}{2 \cdot 4}

a = \frac{- ( - 5 ) + 25 + 16 y}{2 \cdot 4} : \frac{5 + 25 + 16 y}{8}

a = \frac{- ( - 5 ) - 25 + 16 y}{2 \cdot 4} : \frac{5 - 25 + 16 y}{8}

The solutions to the quadratic equation are:

a = \frac{5 + 25 + 16 y}{8}, a = \frac{5 - 25 + 16 y}{8}

3 x^{2} - 15 x - 12 = 0

4 x^{2} - 0.2 = 0

- 6 x^{2} + 5 = - 4 x + 8

18 x^{2} - 18 = 0

3 x^{2} + 7 = - 9 x^{2} + 4

What are the solutions to the equation y=a(4a-5),a=3 ?
The solutions to the equation y=a(4a-5),a=3 are a=(5+sqrt(25+16y))/8 ,a=(5-sqrt(25+16y))/8
Find the zeros of y=a(4a-5),a=3
The zeros of y=a(4a-5),a=3 are a=(5+sqrt(25+16y))/8 ,a=(5-sqrt(25+16y))/8