What are the solutions to the equation (4x-5)(x+2)=4x+1 ?

The solutions to the equation (4x-5)(x+2)=4x+1 are x=(1+sqrt(177))/8 ,x=(1-sqrt(177))/8

Find the zeros of (4x-5)(x+2)=4x+1

The zeros of (4x-5)(x+2)=4x+1 are x=(1+sqrt(177))/8 ,x=(1-sqrt(177))/8

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(4 x - 5) (x + 2) = 4 x + 1

x = \frac{1 + 177}{8}, x = \frac{1 - 177}{8}

Solution steps

(4 x - 5) (x + 2) = 4 x + 1

Expand

(4 x - 5) (x + 2) : 4 x^{2} + 3 x - 10

4 x^{2} + 3 x - 10 = 4 x + 1

Move

1

to the left side

4 x^{2} + 3 x - 11 = 4 x

Move

4 x

to the left side

4 x^{2} - x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 4 ( - 11 )}{2 \cdot 4}

(- 1)^{2} - 4 \cdot 4 (- 11) = 177

x_{1, 2} = \frac{- ( - 1 ) \pm 177}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 177}{2 \cdot 4}, x_{2} = \frac{- ( - 1 ) - 177}{2 \cdot 4}

x = \frac{- ( - 1 ) + 177}{2 \cdot 4} : \frac{1 + 177}{8}

x = \frac{- ( - 1 ) - 177}{2 \cdot 4} : \frac{1 - 177}{8}

The solutions to the quadratic equation are:

x = \frac{1 + 177}{8}, x = \frac{1 - 177}{8}

2 x (x + 3) = x^{2} + 3 x + 70

- x^{2} + 9 x - 3

(x - 2) (x - 3) = 30

y^{2} = 9 y

7 x + 2 (- 9 x + 3) = x - (- 4 x + 6) x - (- 4 x + 6)

What are the solutions to the equation (4x-5)(x+2)=4x+1 ?
The solutions to the equation (4x-5)(x+2)=4x+1 are x=(1+sqrt(177))/8 ,x=(1-sqrt(177))/8
Find the zeros of (4x-5)(x+2)=4x+1
The zeros of (4x-5)(x+2)=4x+1 are x=(1+sqrt(177))/8 ,x=(1-sqrt(177))/8