What are the solutions to the equation ((3x-7)(x+1))/2 =8 ?

The solutions to the equation ((3x-7)(x+1))/2 =8 are x=(2+sqrt(73))/3 ,x=(2-sqrt(73))/3

Find the zeros of ((3x-7)(x+1))/2 =8

The zeros of ((3x-7)(x+1))/2 =8 are x=(2+sqrt(73))/3 ,x=(2-sqrt(73))/3

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\frac{( 3 x - 7 ) ( x + 1 )}{2} = 8

x = \frac{2 + 73}{3}, x = \frac{2 - 73}{3}

Decimal Notation

x = 3.51466 \dots, x = - 2.18133 \dots

Solution steps

\frac{( 3 x - 7 ) ( x + 1 )}{2} = 8

Multiply both sides by

2

(3 x - 7) (x + 1) = 16

Expand

(3 x - 7) (x + 1) : 3 x^{2} - 4 x - 7

3 x^{2} - 4 x - 7 = 16

Move

16

to the left side

3 x^{2} - 4 x - 23 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 ( - 23 )}{2 \cdot 3}

(- 4)^{2} - 4 \cdot 3 (- 23) = 273

x_{1, 2} = \frac{- ( - 4 ) \pm 2 73}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 73}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 73}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 73}{2 \cdot 3} : \frac{2 + 73}{3}

x = \frac{- ( - 4 ) - 2 73}{2 \cdot 3} : \frac{2 - 73}{3}

The solutions to the quadratic equation are:

x = \frac{2 + 73}{3}, x = \frac{2 - 73}{3}

x^{2} = 7 x - 10

(x - 2)^{2} = - 12

5 x^{2} - 54 x + 94 = 2 x^{2} - 5

y^{2} + 16 y + 64 = 0

(2 x + 8) (2 x + 12) = 320

What are the solutions to the equation ((3x-7)(x+1))/2 =8 ?
The solutions to the equation ((3x-7)(x+1))/2 =8 are x=(2+sqrt(73))/3 ,x=(2-sqrt(73))/3
Find the zeros of ((3x-7)(x+1))/2 =8
The zeros of ((3x-7)(x+1))/2 =8 are x=(2+sqrt(73))/3 ,x=(2-sqrt(73))/3