What are the solutions to the equation 1/2 w^2-2/3 = 5/6 w ?

The solutions to the equation 1/2 w^2-2/3 = 5/6 w are w=(5+sqrt(73))/6 ,w=(5-sqrt(73))/6

Find the zeros of 1/2 w^2-2/3 = 5/6 w

The zeros of 1/2 w^2-2/3 = 5/6 w are w=(5+sqrt(73))/6 ,w=(5-sqrt(73))/6

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\frac{1}{2} w^{2} - \frac{2}{3} = \frac{5}{6} w

w = \frac{5 + 73}{6}, w = \frac{5 - 73}{6}

Decimal Notation

w = 2.25733 \dots, w = - 0.59066 \dots

Solution steps

\frac{1}{2} w^{2} - \frac{2}{3} = \frac{5}{6} w

Find Least Common Multiplier of

2, 3, 6 : 6

Multiply by LCM=

6

\frac{1}{2} w^{2} \cdot 6 - \frac{2}{3} \cdot 6 = \frac{5}{6} w \cdot 6

Simplify

3 w^{2} - 4 = 5 w

Move

5 w

to the left side

3 w^{2} - 4 - 5 w = 0

Write in the standard form

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

3 w^{2} - 5 w - 4 = 0

Solve with the quadratic formula

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

(- 5)^{2} - 4 \cdot 3 (- 4) = 73

w_{1, 2} = \frac{- ( - 5 ) \pm 73}{2 \cdot 3}

Separate the solutions

w_{1} = \frac{- ( - 5 ) + 73}{2 \cdot 3}, w_{2} = \frac{- ( - 5 ) - 73}{2 \cdot 3}

w = \frac{- ( - 5 ) + 73}{2 \cdot 3} : \frac{5 + 73}{6}

w = \frac{- ( - 5 ) - 73}{2 \cdot 3} : \frac{5 - 73}{6}

The solutions to the quadratic equation are:

w = \frac{5 + 73}{6}, w = \frac{5 - 73}{6}

x^{2} + 3 x - 154

3 x^{2} + 42 x + 72

43 \geq 6^{2 z - 3}

\frac{w}{2} - 1 \leq 1

- 4 < 3 x + 2 \leq 8

What are the solutions to the equation 1/2 w^2-2/3 = 5/6 w ?
The solutions to the equation 1/2 w^2-2/3 = 5/6 w are w=(5+sqrt(73))/6 ,w=(5-sqrt(73))/6
Find the zeros of 1/2 w^2-2/3 = 5/6 w
The zeros of 1/2 w^2-2/3 = 5/6 w are w=(5+sqrt(73))/6 ,w=(5-sqrt(73))/6