What are the solutions to the equation -19+8x=-4x^2+2x ?

The solutions to the equation -19+8x=-4x^2+2x are x=-(3+sqrt(85))/4 ,x=(sqrt(85)-3)/4

Find the zeros of -19+8x=-4x^2+2x

The zeros of -19+8x=-4x^2+2x are x=-(3+sqrt(85))/4 ,x=(sqrt(85)-3)/4

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- 19 + 8 x = - 4 x^{2} + 2 x

x = - \frac{3 + 85}{4}, x = \frac{85 - 3}{4}

Decimal Notation

x = - 3.05488 \dots, x = 1.55488 \dots

Solution steps

- 19 + 8 x = - 4 x^{2} + 2 x

Switch sides

- 4 x^{2} + 2 x = - 19 + 8 x

Move

8 x

to the left side

- 4 x^{2} - 6 x = - 19

Move

19

to the left side

- 4 x^{2} - 6 x + 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 ( - 4 ) \cdot 19}{2 ( - 4 )}

(- 6)^{2} - 4 (- 4) \cdot 19 = 285

x_{1, 2} = \frac{- ( - 6 ) \pm 2 85}{2 ( - 4 )}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 85}{2 ( - 4 )}, x_{2} = \frac{- ( - 6 ) - 2 85}{2 ( - 4 )}

x = \frac{- ( - 6 ) + 2 85}{2 ( - 4 )} : - \frac{3 + 85}{4}

x = \frac{- ( - 6 ) - 2 85}{2 ( - 4 )} : \frac{85 - 3}{4}

The solutions to the quadratic equation are:

x = - \frac{3 + 85}{4}, x = \frac{85 - 3}{4}

40 x - 7 x^{2} = 101 - 3 x^{2}

x^{2} - 24 x + 108 = 0

8 b^{2} + 59 b + 21 = 0

(x^{2} - 9 x) + (11 x + 12) = 180

b^{2} + 19 b

What are the solutions to the equation -19+8x=-4x^2+2x ?
The solutions to the equation -19+8x=-4x^2+2x are x=-(3+sqrt(85))/4 ,x=(sqrt(85)-3)/4
Find the zeros of -19+8x=-4x^2+2x
The zeros of -19+8x=-4x^2+2x are x=-(3+sqrt(85))/4 ,x=(sqrt(85)-3)/4