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

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

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

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

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4 x^{2} - 11 = 4 x

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} - 11 = 4 x

Move

4 x

to the left side

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

Write in the standard form

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

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}

x^{2} - 2 x - 15

x^{2} - 3 x + 1

13 - x^{2} = - 10

x^{2} + 12 x + 27 = 0

23 p = 5 p^{2} + 24

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