What are the solutions to the equation 12k^2-32k-64=0 ?

The solutions to the equation 12k^2-32k-64=0 are k=4,k=-4/3

Find the zeros of 12k^2-32k-64=0

The zeros of 12k^2-32k-64=0 are k=4,k=-4/3

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12 k^{2} - 32 k - 64 = 0

k = 4, k = - \frac{4}{3}

Decimal Notation

k = 4, k = - 1.33333 \dots

Solution steps

12 k^{2} - 32 k - 64 = 0

Solve with the quadratic formula

k_{1, 2} = \frac{- ( - 32 ) \pm ( - 32 ) ^{2} - 4 \cdot 12 ( - 64 )}{2 \cdot 12}

(- 32)^{2} - 4 \cdot 12 (- 64) = 64

k_{1, 2} = \frac{- ( - 32 ) \pm 64}{2 \cdot 12}

Separate the solutions

k_{1} = \frac{- ( - 32 ) + 64}{2 \cdot 12}, k_{2} = \frac{- ( - 32 ) - 64}{2 \cdot 12}

k = \frac{- ( - 32 ) + 64}{2 \cdot 12} : 4

k = \frac{- ( - 32 ) - 64}{2 \cdot 12} : - \frac{4}{3}

The solutions to the quadratic equation are:

k = 4, k = - \frac{4}{3}

(x) = x^{2} - 6 x + 5

x = 3 x^{2} - 2, y = \frac{ln ( x ) , d y}{d x}

- 5 x^{2} + 12 x - 4 = 0

- 2 x^{2} - 40 x - 128 = 0

4 x^{2} + 6 x + 15 = 0

What are the solutions to the equation 12k^2-32k-64=0 ?
The solutions to the equation 12k^2-32k-64=0 are k=4,k=-4/3
Find the zeros of 12k^2-32k-64=0
The zeros of 12k^2-32k-64=0 are k=4,k=-4/3