What are the solutions to the equation 4x^2+1=12x ?

The solutions to the equation 4x^2+1=12x are x=(3+2sqrt(2))/2 ,x=(3-2sqrt(2))/2

Find the zeros of 4x^2+1=12x

The zeros of 4x^2+1=12x are x=(3+2sqrt(2))/2 ,x=(3-2sqrt(2))/2

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4 x^{2} + 1 = 12 x

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

Solution steps

4 x^{2} + 1 = 12 x

Move

12 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 12)^{2} - 4 \cdot 4 \cdot 1 = 82

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

x^{2} - x = 72

x^{3} - 4 x + 15

\frac{x ^{5}}{x ^{7}}

20 x^{2} + 55 x + 30

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