What are the solutions to the equation 4x^2-12x-11=0 ?

The solutions to the equation 4x^2-12x-11=0 are x=(3+2sqrt(5))/2 ,x=(3-2sqrt(5))/2

Find the zeros of 4x^2-12x-11=0

The zeros of 4x^2-12x-11=0 are x=(3+2sqrt(5))/2 ,x=(3-2sqrt(5))/2

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4 x^{2} - 12 x - 11 = 0

x = \frac{3 + 2 5}{2}, x = \frac{3 - 2 5}{2}

Decimal Notation

x = 3.73606 \dots, x = - 0.73606 \dots

Solution steps

4 x^{2} - 12 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 4 ( - 11 )}{2 \cdot 4}

(- 12)^{2} - 4 \cdot 4 (- 11) = 85

x_{1, 2} = \frac{- ( - 12 ) \pm 8 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 8 5}{2 \cdot 4}, x_{2} = \frac{- ( - 12 ) - 8 5}{2 \cdot 4}

x = \frac{- ( - 12 ) + 8 5}{2 \cdot 4} : \frac{3 + 2 5}{2}

x = \frac{- ( - 12 ) - 8 5}{2 \cdot 4} : \frac{3 - 2 5}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 2 5}{2}, x = \frac{3 - 2 5}{2}

- 3.1 x^{2} + 4.5 x - 19.9 = 750

lo g_{6} (\frac{1}{216}) = x

2 a^{2} - 3 ab - 2 b^{2}

3 f \leq 15

4 x + 7 x - 40 = 60 - 9 x

What are the solutions to the equation 4x^2-12x-11=0 ?
The solutions to the equation 4x^2-12x-11=0 are x=(3+2sqrt(5))/2 ,x=(3-2sqrt(5))/2
Find the zeros of 4x^2-12x-11=0
The zeros of 4x^2-12x-11=0 are x=(3+2sqrt(5))/2 ,x=(3-2sqrt(5))/2