What are the solutions to the equation 48= 1/2 b(3b-2) ?

The solutions to the equation 48= 1/2 b(3b-2) are b=6,b=-16/3

Find the zeros of 48= 1/2 b(3b-2)

The zeros of 48= 1/2 b(3b-2) are b=6,b=-16/3

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48 = \frac{1}{2} b (3 b - 2)

b = 6, b = - \frac{16}{3}

Decimal Notation

b = 6, b = - 5.33333 \dots

Solution steps

48 = \frac{1}{2} b (3 b - 2)

Multiply both sides by

2

96 = b (3 b - 2)

Expand

b (3 b - 2) : 3 b^{2} - 2 b

96 = 3 b^{2} - 2 b

Switch sides

3 b^{2} - 2 b = 96

Move

96

to the left side

3 b^{2} - 2 b - 96 = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 3 ( - 96 )}{2 \cdot 3}

(- 2)^{2} - 4 \cdot 3 (- 96) = 34

b_{1, 2} = \frac{- ( - 2 ) \pm 34}{2 \cdot 3}

Separate the solutions

b_{1} = \frac{- ( - 2 ) + 34}{2 \cdot 3}, b_{2} = \frac{- ( - 2 ) - 34}{2 \cdot 3}

b = \frac{- ( - 2 ) + 34}{2 \cdot 3} : 6

b = \frac{- ( - 2 ) - 34}{2 \cdot 3} : - \frac{16}{3}

The solutions to the quadratic equation are:

b = 6, b = - \frac{16}{3}

4 x^{2} + 8 x - 17 = x^{2} - 2 x

\frac{9}{9 ^{- \frac{4}{5}}}

\frac{3}{2} \cdot 9

3 x^{2} - 36 x = 0

\frac{4}{3 x - 2} \leq \frac{2}{x + 1}

What are the solutions to the equation 48= 1/2 b(3b-2) ?
The solutions to the equation 48= 1/2 b(3b-2) are b=6,b=-16/3
Find the zeros of 48= 1/2 b(3b-2)
The zeros of 48= 1/2 b(3b-2) are b=6,b=-16/3