What are the solutions to the equation w(3w-4)=54 ?

The solutions to the equation w(3w-4)=54 are w=(2+sqrt(166))/3 ,w=(2-sqrt(166))/3

Find the zeros of w(3w-4)=54

The zeros of w(3w-4)=54 are w=(2+sqrt(166))/3 ,w=(2-sqrt(166))/3

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w (3 w - 4) = 54

w = \frac{2 + 166}{3}, w = \frac{2 - 166}{3}

Decimal Notation

w = 4.96136 \dots, w = - 3.62803 \dots

Solution steps

w (3 w - 4) = 54

Expand

w (3 w - 4) : 3 w^{2} - 4 w

3 w^{2} - 4 w = 54

Move

54

to the left side

3 w^{2} - 4 w - 54 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 ( - 54 )}{2 \cdot 3}

(- 4)^{2} - 4 \cdot 3 (- 54) = 2166

w_{1, 2} = \frac{- ( - 4 ) \pm 2 166}{2 \cdot 3}

Separate the solutions

w_{1} = \frac{- ( - 4 ) + 2 166}{2 \cdot 3}, w_{2} = \frac{- ( - 4 ) - 2 166}{2 \cdot 3}

w = \frac{- ( - 4 ) + 2 166}{2 \cdot 3} : \frac{2 + 166}{3}

w = \frac{- ( - 4 ) - 2 166}{2 \cdot 3} : \frac{2 - 166}{3}

The solutions to the quadratic equation are:

w = \frac{2 + 166}{3}, w = \frac{2 - 166}{3}

\frac{6}{7} w = 42

6 x^{2} + 42 x = 0

\frac{8}{- 2 + i}

- \frac{5}{4} = x - \frac{7}{10}

2 b^{2} - 5 b + 3

What are the solutions to the equation w(3w-4)=54 ?
The solutions to the equation w(3w-4)=54 are w=(2+sqrt(166))/3 ,w=(2-sqrt(166))/3
Find the zeros of w(3w-4)=54
The zeros of w(3w-4)=54 are w=(2+sqrt(166))/3 ,w=(2-sqrt(166))/3