What are the solutions to the equation 6x^2-12x=3 ?

The solutions to the equation 6x^2-12x=3 are x=(2+sqrt(6))/2 ,x=(2-sqrt(6))/2

Find the zeros of 6x^2-12x=3

The zeros of 6x^2-12x=3 are x=(2+sqrt(6))/2 ,x=(2-sqrt(6))/2

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6 x^{2} - 12 x = 3

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}

Decimal Notation

x = 2.22474 \dots, x = - 0.22474 \dots

Solution steps

6 x^{2} - 12 x = 3

Move

3

to the left side

6 x^{2} - 12 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 6 ( - 3 )}{2 \cdot 6}

(- 12)^{2} - 4 \cdot 6 (- 3) = 66

x_{1, 2} = \frac{- ( - 12 ) \pm 6 6}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 6 6}{2 \cdot 6}, x_{2} = \frac{- ( - 12 ) - 6 6}{2 \cdot 6}

x = \frac{- ( - 12 ) + 6 6}{2 \cdot 6} : \frac{2 + 6}{2}

x = \frac{- ( - 12 ) - 6 6}{2 \cdot 6} : \frac{2 - 6}{2}

The solutions to the quadratic equation are:

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}

12 x^{2} + 12 x + 3 = 0

10 - (x - 3)^{2} = 5

4 x^{2} = 20 x - 25

8 x^{2} - 6 x - 9 = 0

4 x^{2} - 23 x + 15 = 0

What are the solutions to the equation 6x^2-12x=3 ?
The solutions to the equation 6x^2-12x=3 are x=(2+sqrt(6))/2 ,x=(2-sqrt(6))/2
Find the zeros of 6x^2-12x=3
The zeros of 6x^2-12x=3 are x=(2+sqrt(6))/2 ,x=(2-sqrt(6))/2