What are the solutions to the equation 3(x-3)(x+3)=2(x-1) ?

The solutions to the equation 3(x-3)(x+3)=2(x-1) are x=(1+2sqrt(19))/3 ,x=(1-2sqrt(19))/3

Find the zeros of 3(x-3)(x+3)=2(x-1)

The zeros of 3(x-3)(x+3)=2(x-1) are x=(1+2sqrt(19))/3 ,x=(1-2sqrt(19))/3

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3 (x - 3) (x + 3) = 2 (x - 1)

x = \frac{1 + 2 19}{3}, x = \frac{1 - 2 19}{3}

Decimal Notation

x = 3.23926 \dots, x = - 2.57259 \dots

Solution steps

3 (x - 3) (x + 3) = 2 (x - 1)

Expand

3 (x - 3) (x + 3) : 3 x^{2} - 27

Expand

2 (x - 1) : 2 x - 2

3 x^{2} - 27 = 2 x - 2

Move

2

to the left side

3 x^{2} - 25 = 2 x

Move

2 x

to the left side

3 x^{2} - 25 - 2 x = 0

Write in the standard form

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

3 x^{2} - 2 x - 25 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 3 ( - 25 )}{2 \cdot 3}

(- 2)^{2} - 4 \cdot 3 (- 25) = 419

x_{1, 2} = \frac{- ( - 2 ) \pm 4 19}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 4 19}{2 \cdot 3}, x_{2} = \frac{- ( - 2 ) - 4 19}{2 \cdot 3}

x = \frac{- ( - 2 ) + 4 19}{2 \cdot 3} : \frac{1 + 2 19}{3}

x = \frac{- ( - 2 ) - 4 19}{2 \cdot 3} : \frac{1 - 2 19}{3}

The solutions to the quadratic equation are:

x = \frac{1 + 2 19}{3}, x = \frac{1 - 2 19}{3}

6 (2 - x) = 2 x + 4

- 2 q^{4} + 2 q^{3} + q^{2} - 1

a^{2} + 11 a + 30 = 0

\frac{2}{\frac{5}{3}}

x^{4} + 3 x^{3} + x^{2} + 4 x + 3

What are the solutions to the equation 3(x-3)(x+3)=2(x-1) ?
The solutions to the equation 3(x-3)(x+3)=2(x-1) are x=(1+2sqrt(19))/3 ,x=(1-2sqrt(19))/3
Find the zeros of 3(x-3)(x+3)=2(x-1)
The zeros of 3(x-3)(x+3)=2(x-1) are x=(1+2sqrt(19))/3 ,x=(1-2sqrt(19))/3