What are the solutions to the equation 6x+9=2x^2 ?

The solutions to the equation 6x+9=2x^2 are x=(3(1+sqrt(3)))/2 ,x=(3(1-sqrt(3)))/2

Find the zeros of 6x+9=2x^2

The zeros of 6x+9=2x^2 are x=(3(1+sqrt(3)))/2 ,x=(3(1-sqrt(3)))/2

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6 x + 9 = 2 x^{2}

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

Decimal Notation

x = 4.09807 \dots, x = - 1.09807 \dots

Solution steps

6 x + 9 = 2 x^{2}

Switch sides

2 x^{2} = 6 x + 9

Move

9

to the left side

2 x^{2} - 9 = 6 x

Move

6 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 ( - 9 )}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 (- 9) = 63

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

Separate the solutions

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

x = \frac{- ( - 6 ) + 6 3}{2 \cdot 2} : \frac{3 ( 1 + 3 )}{2}

x = \frac{- ( - 6 ) - 6 3}{2 \cdot 2} : \frac{3 ( 1 - 3 )}{2}

The solutions to the quadratic equation are:

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

x, z = 2 x^{2} + y^{2}

- 11 = x^{2} - 36

x^{2} - 5 x - 24 = 0

3 x (x + 4) + (x + 4)^{2} = 0

6 y^{2} + 4 y

What are the solutions to the equation 6x+9=2x^2 ?
The solutions to the equation 6x+9=2x^2 are x=(3(1+sqrt(3)))/2 ,x=(3(1-sqrt(3)))/2
Find the zeros of 6x+9=2x^2
The zeros of 6x+9=2x^2 are x=(3(1+sqrt(3)))/2 ,x=(3(1-sqrt(3)))/2