What are the solutions to the equation 12x^2-1=8x ?

The solutions to the equation 12x^2-1=8x are x=(2+sqrt(7))/6 ,x=(2-sqrt(7))/6

Find the zeros of 12x^2-1=8x

The zeros of 12x^2-1=8x are x=(2+sqrt(7))/6 ,x=(2-sqrt(7))/6

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12 x^{2} - 1 = 8 x

x = \frac{2 + 7}{6}, x = \frac{2 - 7}{6}

Decimal Notation

x = 0.77429 \dots, x = - 0.10762 \dots

Solution steps

12 x^{2} - 1 = 8 x

Move

8 x

to the left side

12 x^{2} - 1 - 8 x = 0

Write in the standard form

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

12 x^{2} - 8 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 12 ( - 1 )}{2 \cdot 12}

(- 8)^{2} - 4 \cdot 12 (- 1) = 47

x_{1, 2} = \frac{- ( - 8 ) \pm 4 7}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 7}{2 \cdot 12}, x_{2} = \frac{- ( - 8 ) - 4 7}{2 \cdot 12}

x = \frac{- ( - 8 ) + 4 7}{2 \cdot 12} : \frac{2 + 7}{6}

x = \frac{- ( - 8 ) - 4 7}{2 \cdot 12} : \frac{2 - 7}{6}

The solutions to the quadratic equation are:

x = \frac{2 + 7}{6}, x = \frac{2 - 7}{6}

x^{2} - 10 x - 35 = - 8 x

x^{2} + 2.4 x + a = 0

(2 - 3 d) (4 - 3 d) = 0

(x + 3)^{2} = 2

x^{2} - 3 x - \frac{9}{4} = 12

What are the solutions to the equation 12x^2-1=8x ?
The solutions to the equation 12x^2-1=8x are x=(2+sqrt(7))/6 ,x=(2-sqrt(7))/6
Find the zeros of 12x^2-1=8x
The zeros of 12x^2-1=8x are x=(2+sqrt(7))/6 ,x=(2-sqrt(7))/6