What are the solutions to the equation (2x-7)(x-6)=18 ?

The solutions to the equation (2x-7)(x-6)=18 are x=8,x= 3/2

Find the zeros of (2x-7)(x-6)=18

The zeros of (2x-7)(x-6)=18 are x=8,x= 3/2

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(2 x - 7) (x - 6) = 18

x = 8, x = \frac{3}{2}

Decimal Notation

x = 8, x = 1.5

Solution steps

(2 x - 7) (x - 6) = 18

Expand

(2 x - 7) (x - 6) : 2 x^{2} - 19 x + 42

2 x^{2} - 19 x + 42 = 18

Move

18

to the left side

2 x^{2} - 19 x + 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 19 ) \pm ( - 19 ) ^{2} - 4 \cdot 2 \cdot 24}{2 \cdot 2}

(- 19)^{2} - 4 \cdot 2 \cdot 24 = 13

x_{1, 2} = \frac{- ( - 19 ) \pm 13}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 19 ) + 13}{2 \cdot 2}, x_{2} = \frac{- ( - 19 ) - 13}{2 \cdot 2}

x = \frac{- ( - 19 ) + 13}{2 \cdot 2} : 8

x = \frac{- ( - 19 ) - 13}{2 \cdot 2} : \frac{3}{2}

The solutions to the quadratic equation are:

x = 8, x = \frac{3}{2}

x^{2} - 4 x + 10

- 3 x = - 10 x^{2} - 4

(x - 3)^{2} = 100

2 x^{2} + 3 x + 12 = 0

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

What are the solutions to the equation (2x-7)(x-6)=18 ?
The solutions to the equation (2x-7)(x-6)=18 are x=8,x= 3/2
Find the zeros of (2x-7)(x-6)=18
The zeros of (2x-7)(x-6)=18 are x=8,x= 3/2