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

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

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

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

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

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

Decimal Notation

x = 0.33333 \dots, x = - 0.25

Solution steps

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

9 x^{2} + 31 x + 12 \leq 0

x + 1 = 3 x + 1

∣ 5 x + 3 ∣ < 2

\frac{11 - 5 x}{8} - \frac{6 x - 3}{4} = \frac{4 x - 1}{8}

15 t^{2} + 5 t = 0

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