What are the solutions to the equation 12w^2-1w-1=0 ?

The solutions to the equation 12w^2-1w-1=0 are w= 1/3 ,w=-1/4

Find the zeros of 12w^2-1w-1=0

The zeros of 12w^2-1w-1=0 are w= 1/3 ,w=-1/4

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12 w^{2} - 1 w - 1 = 0

w = \frac{1}{3}, w = - \frac{1}{4}

Decimal Notation

w = 0.33333 \dots, w = - 0.25

Solution steps

12 w^{2} - 1 \cdot w - 1 = 0

Refine

12 w^{2} - w - 1 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 12 ( - 1 )}{2 \cdot 12}

(- 1)^{2} - 4 \cdot 12 (- 1) = 7

w_{1, 2} = \frac{- ( - 1 ) \pm 7}{2 \cdot 12}

Separate the solutions

w_{1} = \frac{- ( - 1 ) + 7}{2 \cdot 12}, w_{2} = \frac{- ( - 1 ) - 7}{2 \cdot 12}

w = \frac{- ( - 1 ) + 7}{2 \cdot 12} : \frac{1}{3}

w = \frac{- ( - 1 ) - 7}{2 \cdot 12} : - \frac{1}{4}

The solutions to the quadratic equation are:

w = \frac{1}{3}, w = - \frac{1}{4}

3 x^{2} + 55 = 0

0 = - 16 x^{2} + 35 x + 6.5

(3 x + 1)^{2} - 16 = 0

z^{2} = - 49

29 x^{2} - 4 x + 1 = 0

What are the solutions to the equation 12w^2-1w-1=0 ?
The solutions to the equation 12w^2-1w-1=0 are w= 1/3 ,w=-1/4
Find the zeros of 12w^2-1w-1=0
The zeros of 12w^2-1w-1=0 are w= 1/3 ,w=-1/4