What are the solutions to the equation 9x^2=11+6x ?

The solutions to the equation 9x^2=11+6x are x=(1+2sqrt(3))/3 ,x=(1-2sqrt(3))/3

Find the zeros of 9x^2=11+6x

The zeros of 9x^2=11+6x are x=(1+2sqrt(3))/3 ,x=(1-2sqrt(3))/3

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9 x^{2} = 11 + 6 x

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

Decimal Notation

x = 1.48803 \dots, x = - 0.82136 \dots

Solution steps

9 x^{2} = 11 + 6 x

Move

6 x

to the left side

9 x^{2} - 6 x = 11

Move

11

to the left side

9 x^{2} - 6 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 9 ( - 11 )}{2 \cdot 9}

(- 6)^{2} - 4 \cdot 9 (- 11) = 123

x_{1, 2} = \frac{- ( - 6 ) \pm 12 3}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 12 3}{2 \cdot 9}, x_{2} = \frac{- ( - 6 ) - 12 3}{2 \cdot 9}

x = \frac{- ( - 6 ) + 12 3}{2 \cdot 9} : \frac{1 + 2 3}{3}

x = \frac{- ( - 6 ) - 12 3}{2 \cdot 9} : \frac{1 - 2 3}{3}

The solutions to the quadratic equation are:

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

x, 2 x^{2} h = 1000

A (x) = (x - 5) (x + 7)

3 x^{2} + 660 x - 15 = 0

6 y^{2} + 3 y + 24 = 0

- x^{2} - 9 x + 18 = 0

What are the solutions to the equation 9x^2=11+6x ?
The solutions to the equation 9x^2=11+6x are x=(1+2sqrt(3))/3 ,x=(1-2sqrt(3))/3
Find the zeros of 9x^2=11+6x
The zeros of 9x^2=11+6x are x=(1+2sqrt(3))/3 ,x=(1-2sqrt(3))/3