What are the solutions to the equation 4x(3x-1)=1 ?

The solutions to the equation 4x(3x-1)=1 are x= 1/2 ,x=-1/6

Find the zeros of 4x(3x-1)=1

The zeros of 4x(3x-1)=1 are x= 1/2 ,x=-1/6

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4 x (3 x - 1) = 1

x = \frac{1}{2}, x = - \frac{1}{6}

Decimal Notation

x = 0.5, x = - 0.16666 \dots

Solution steps

4 x (3 x - 1) = 1

Expand

4 x (3 x - 1) : 12 x^{2} - 4 x

12 x^{2} - 4 x = 1

Move

1

to the left side

12 x^{2} - 4 x - 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

x = \frac{- ( - 4 ) + 8}{2 \cdot 12} : \frac{1}{2}

x = \frac{- ( - 4 ) - 8}{2 \cdot 12} : - \frac{1}{6}

The solutions to the quadratic equation are:

x = \frac{1}{2}, x = - \frac{1}{6}

\frac{( 6 - 7 i )}{( 4 - 5 i )}

x^{2} - 30 - x = 0

x^{4} - x^{3} - 13 x^{2} + 25 x - 12

\frac{x + 6}{x - 1} > 0

x^{4} + x^{2} - 72

What are the solutions to the equation 4x(3x-1)=1 ?
The solutions to the equation 4x(3x-1)=1 are x= 1/2 ,x=-1/6
Find the zeros of 4x(3x-1)=1
The zeros of 4x(3x-1)=1 are x= 1/2 ,x=-1/6