What are the solutions to the equation 2(x+3)(x-4)=6x+6 ?

The solutions to the equation 2(x+3)(x-4)=6x+6 are x=2+sqrt(19),x=2-sqrt(19)

Find the zeros of 2(x+3)(x-4)=6x+6

The zeros of 2(x+3)(x-4)=6x+6 are x=2+sqrt(19),x=2-sqrt(19)

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2 (x + 3) (x - 4) = 6 x + 6

x = 2 + 19, x = 2 - 19

Decimal Notation

x = 6.35889 \dots, x = - 2.35889 \dots

Solution steps

2 (x + 3) (x - 4) = 6 x + 6

Expand

2 (x + 3) (x - 4) : 2 x^{2} - 2 x - 24

2 x^{2} - 2 x - 24 = 6 x + 6

Move

6

to the left side

2 x^{2} - 2 x - 30 = 6 x

Move

6 x

to the left side

2 x^{2} - 8 x - 30 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 2 ( - 30 )}{2 \cdot 2}

(- 8)^{2} - 4 \cdot 2 (- 30) = 419

x_{1, 2} = \frac{- ( - 8 ) \pm 4 19}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 19}{2 \cdot 2}, x_{2} = \frac{- ( - 8 ) - 4 19}{2 \cdot 2}

x = \frac{- ( - 8 ) + 4 19}{2 \cdot 2} : 2 + 19

x = \frac{- ( - 8 ) - 4 19}{2 \cdot 2} : 2 - 19

The solutions to the quadratic equation are:

x = 2 + 19, x = 2 - 19

9 x^{2} + 6 x + 3 = 0

3 y^{2} + 10 y + 7 = 0

(x - 7)^{2} = 8

\frac{1}{2} x^{2} + 3 = 75

m^{2} + 18 m + 75 = - 2

What are the solutions to the equation 2(x+3)(x-4)=6x+6 ?
The solutions to the equation 2(x+3)(x-4)=6x+6 are x=2+sqrt(19),x=2-sqrt(19)
Find the zeros of 2(x+3)(x-4)=6x+6
The zeros of 2(x+3)(x-4)=6x+6 are x=2+sqrt(19),x=2-sqrt(19)