What are the solutions to the equation -3(x-2)-4x^2=0 ?

The solutions to the equation -3(x-2)-4x^2=0 are x=-(3+sqrt(105))/8 ,x=(sqrt(105)-3)/8

Find the zeros of -3(x-2)-4x^2=0

The zeros of -3(x-2)-4x^2=0 are x=-(3+sqrt(105))/8 ,x=(sqrt(105)-3)/8

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- 3 (x - 2) - 4 x^{2} = 0

x = - \frac{3 + 105}{8}, x = \frac{105 - 3}{8}

Decimal Notation

x = - 1.65586 \dots, x = 0.90586 \dots

Solution steps

- 3 (x - 2) - 4 x^{2} = 0

Expand

- 3 (x - 2) - 4 x^{2} : - 3 x + 6 - 4 x^{2}

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

Write in the standard form

a x^{2} + b x + c = 0

- 4 x^{2} - 3 x + 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 ( - 4 ) \cdot 6}{2 ( - 4 )}

(- 3)^{2} - 4 (- 4) \cdot 6 = 105

x_{1, 2} = \frac{- ( - 3 ) \pm 105}{2 ( - 4 )}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 105}{2 ( - 4 )}, x_{2} = \frac{- ( - 3 ) - 105}{2 ( - 4 )}

x = \frac{- ( - 3 ) + 105}{2 ( - 4 )} : - \frac{3 + 105}{8}

x = \frac{- ( - 3 ) - 105}{2 ( - 4 )} : \frac{105 - 3}{8}

The solutions to the quadratic equation are:

x = - \frac{3 + 105}{8}, x = \frac{105 - 3}{8}

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

4 x^{2} + 4 x + 1 = 0

(2 x - 8) (2 x + 8) = 55

t^{2} + 8 t + 16 = 0

0 = 0.03 q^{2} + 35 q - 712

What are the solutions to the equation -3(x-2)-4x^2=0 ?
The solutions to the equation -3(x-2)-4x^2=0 are x=-(3+sqrt(105))/8 ,x=(sqrt(105)-3)/8
Find the zeros of -3(x-2)-4x^2=0
The zeros of -3(x-2)-4x^2=0 are x=-(3+sqrt(105))/8 ,x=(sqrt(105)-3)/8