What are the solutions to the equation 3x(x-2)-(x+3)=23(x-3) ?

The solutions to the equation 3x(x-2)-(x+3)=23(x-3) are x=5+sqrt(3),x=5-sqrt(3)

Find the zeros of 3x(x-2)-(x+3)=23(x-3)

The zeros of 3x(x-2)-(x+3)=23(x-3) are x=5+sqrt(3),x=5-sqrt(3)

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3 x (x - 2) - (x + 3) = 23 (x - 3)

x = 5 + 3, x = 5 - 3

Decimal Notation

x = 6.73205 \dots, x = 3.26794 \dots

Solution steps

3 x (x - 2) - (x + 3) = 23 (x - 3)

Expand

3 x (x - 2) - (x + 3) : 3 x^{2} - 7 x - 3

Expand

23 (x - 3) : 23 x - 69

3 x^{2} - 7 x - 3 = 23 x - 69

Move

69

to the left side

3 x^{2} - 7 x + 66 = 23 x

Move

23 x

to the left side

3 x^{2} - 30 x + 66 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 30 ) \pm ( - 30 ) ^{2} - 4 \cdot 3 \cdot 66}{2 \cdot 3}

(- 30)^{2} - 4 \cdot 3 \cdot 66 = 63

x_{1, 2} = \frac{- ( - 30 ) \pm 6 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 30 ) + 6 3}{2 \cdot 3}, x_{2} = \frac{- ( - 30 ) - 6 3}{2 \cdot 3}

x = \frac{- ( - 30 ) + 6 3}{2 \cdot 3} : 5 + 3

x = \frac{- ( - 30 ) - 6 3}{2 \cdot 3} : 5 - 3

The solutions to the quadratic equation are:

x = 5 + 3, x = 5 - 3

x^{2} = 21 - 4 x

(x - 1) (x + 12) = 42

- 3 y + 4 = y^{2}

3 (x + 2) (x - 2) = (x - 4) 2 + 8 x

3 x^{2} + 27 x + 54 = - \frac{3 x ^{2}}{2} - \frac{27 x}{2} - 27

What are the solutions to the equation 3x(x-2)-(x+3)=23(x-3) ?
The solutions to the equation 3x(x-2)-(x+3)=23(x-3) are x=5+sqrt(3),x=5-sqrt(3)
Find the zeros of 3x(x-2)-(x+3)=23(x-3)
The zeros of 3x(x-2)-(x+3)=23(x-3) are x=5+sqrt(3),x=5-sqrt(3)