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} - 11 - 6 x = 0

Write in the standard form

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

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 - 5 ∣ = 0.03

\frac{4}{3} + 3

5 x^{3} + 15 x^{2} + 10 x

(x + 7) (x - 1) = (x + 1)^{2}

x w - y w + x z - yz

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