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

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

Find the zeros of 6x=2x^2+3

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

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6 x = 2 x^{2} + 3

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

Solution steps

6 x = 2 x^{2} + 3

Switch sides

2 x^{2} + 3 = 6 x

Move

6 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 2 \cdot 3 = 23

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

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 3}{2 \cdot 2} : \frac{3 + 3}{2}

x = \frac{- ( - 6 ) - 2 3}{2 \cdot 2} : \frac{3 - 3}{2}

The solutions to the quadratic equation are:

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

2 x + 3 = (x - 1)^{2} - 3

(x + 3)^{2} - 2 = 0

3 x^{2} + 60 = 36 x

49 x^{2} + 70 x + 25 = 0

a^{2} + 3 a + 2 = 0

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