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

The solutions to the equation 4x^2-4x=11 are x=(1+2sqrt(3))/2 ,x=(1-2sqrt(3))/2

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

The zeros of 4x^2-4x=11 are x=(1+2sqrt(3))/2 ,x=(1-2sqrt(3))/2

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4 x^{2} - 4 x = 11

x = \frac{1 + 2 3}{2}, x = \frac{1 - 2 3}{2}

Decimal Notation

x = 2.23205 \dots, x = - 1.23205 \dots

Solution steps

4 x^{2} - 4 x = 11

Move

11

to the left side

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

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 4 (- 11) = 83

x_{1, 2} = \frac{- ( - 4 ) \pm 8 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 8 3}{2 \cdot 4}, x_{2} = \frac{- ( - 4 ) - 8 3}{2 \cdot 4}

x = \frac{- ( - 4 ) + 8 3}{2 \cdot 4} : \frac{1 + 2 3}{2}

x = \frac{- ( - 4 ) - 8 3}{2 \cdot 4} : \frac{1 - 2 3}{2}

The solutions to the quadratic equation are:

x = \frac{1 + 2 3}{2}, x = \frac{1 - 2 3}{2}

9 k^{2} + 42 k - 15 = 0

4 y^{2} + 17 y + 12 = 0

3 x^{2} + 228 = 54 x

y, 2 x y^{2} - 3 x^{2} y = 6 x

8 x - 2 x^{2} = 1

What are the solutions to the equation 4x^2-4x=11 ?
The solutions to the equation 4x^2-4x=11 are x=(1+2sqrt(3))/2 ,x=(1-2sqrt(3))/2
Find the zeros of 4x^2-4x=11
The zeros of 4x^2-4x=11 are x=(1+2sqrt(3))/2 ,x=(1-2sqrt(3))/2