What are the solutions to the equation (3x-4)(x+3)-(x-2)^2=3 ?

The solutions to the equation (3x-4)(x+3)-(x-2)^2=3 are x=(-9+sqrt(233))/4 ,x=(-9-sqrt(233))/4

Find the zeros of (3x-4)(x+3)-(x-2)^2=3

The zeros of (3x-4)(x+3)-(x-2)^2=3 are x=(-9+sqrt(233))/4 ,x=(-9-sqrt(233))/4

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(3 x - 4) (x + 3) - (x - 2)^{2} = 3

x = \frac{- 9 + 233}{4}, x = \frac{- 9 - 233}{4}

Decimal Notation

x = 1.56608 \dots, x = - 6.06608 \dots

Solution steps

(3 x - 4) (x + 3) - (x - 2)^{2} = 3

Expand

(3 x - 4) (x + 3) - (x - 2)^{2} : 2 x^{2} + 9 x - 16

2 x^{2} + 9 x - 16 = 3

Move

3

to the left side

2 x^{2} + 9 x - 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 2 ( - 19 )}{2 \cdot 2}

9^{2} - 4 \cdot 2 (- 19) = 233

x_{1, 2} = \frac{- 9 \pm 233}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 9 + 233}{2 \cdot 2}, x_{2} = \frac{- 9 - 233}{2 \cdot 2}

x = \frac{- 9 + 233}{2 \cdot 2} : \frac{- 9 + 233}{4}

x = \frac{- 9 - 233}{2 \cdot 2} : \frac{- 9 - 233}{4}

The solutions to the quadratic equation are:

x = \frac{- 9 + 233}{4}, x = \frac{- 9 - 233}{4}

2 x^{2} + 10 x + 17 = 0

- x^{2} + 2 x = 1

18 - 2 x^{2} = - 28

x, x^{2} - 4 x + 3 = 0

- 2 x^{2} + 6 x - 7 = 0

What are the solutions to the equation (3x-4)(x+3)-(x-2)^2=3 ?
The solutions to the equation (3x-4)(x+3)-(x-2)^2=3 are x=(-9+sqrt(233))/4 ,x=(-9-sqrt(233))/4
Find the zeros of (3x-4)(x+3)-(x-2)^2=3
The zeros of (3x-4)(x+3)-(x-2)^2=3 are x=(-9+sqrt(233))/4 ,x=(-9-sqrt(233))/4