What are the solutions to the equation 9x^2=4x+2 ?

The solutions to the equation 9x^2=4x+2 are x=(2+sqrt(22))/9 ,x=(2-sqrt(22))/9

Find the zeros of 9x^2=4x+2

The zeros of 9x^2=4x+2 are x=(2+sqrt(22))/9 ,x=(2-sqrt(22))/9

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9 x^{2} = 4 x + 2

x = \frac{2 + 22}{9}, x = \frac{2 - 22}{9}

Decimal Notation

x = 0.74337 \dots, x = - 0.29893 \dots

Solution steps

9 x^{2} = 4 x + 2

Move

2

to the left side

9 x^{2} - 2 = 4 x

Move

4 x

to the left side

9 x^{2} - 2 - 4 x = 0

Write in the standard form

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

9 x^{2} - 4 x - 2 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 9 (- 2) = 222

x_{1, 2} = \frac{- ( - 4 ) \pm 2 22}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 22}{2 \cdot 9}, x_{2} = \frac{- ( - 4 ) - 2 22}{2 \cdot 9}

x = \frac{- ( - 4 ) + 2 22}{2 \cdot 9} : \frac{2 + 22}{9}

x = \frac{- ( - 4 ) - 2 22}{2 \cdot 9} : \frac{2 - 22}{9}

The solutions to the quadratic equation are:

x = \frac{2 + 22}{9}, x = \frac{2 - 22}{9}

x - \frac{1}{2} \leq - \frac{5}{8}

\frac{1}{12} + \frac{7}{12}

(x - 10) (x - 6) = - 4

- 4 c^{2} + 19 c + 5

x^{2} + 13 x + 22 = 7

What are the solutions to the equation 9x^2=4x+2 ?
The solutions to the equation 9x^2=4x+2 are x=(2+sqrt(22))/9 ,x=(2-sqrt(22))/9
Find the zeros of 9x^2=4x+2
The zeros of 9x^2=4x+2 are x=(2+sqrt(22))/9 ,x=(2-sqrt(22))/9