What are the solutions to the equation 4x-2x^2=-32/3 ?

The solutions to the equation 4x-2x^2=-32/3 are x=-(-3+sqrt(57))/3 ,x=(3+sqrt(57))/3

Find the zeros of 4x-2x^2=-32/3

The zeros of 4x-2x^2=-32/3 are x=-(-3+sqrt(57))/3 ,x=(3+sqrt(57))/3

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4 x - 2 x^{2} = - \frac{32}{3}

x = - \frac{- 3 + 57}{3}, x = \frac{3 + 57}{3}

Decimal Notation

x = - 1.51661 \dots, x = 3.51661 \dots

Solution steps

4 x - 2 x^{2} = - \frac{32}{3}

Multiply both sides by

3

12 x - 6 x^{2} = - 32

Move

32

to the left side

12 x - 6 x^{2} + 32 = 0

Write in the standard form

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

- 6 x^{2} + 12 x + 32 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 ( - 6 ) \cdot 32}{2 ( - 6 )}

1 2^{2} - 4 (- 6) \cdot 32 = 457

x_{1, 2} = \frac{- 12 \pm 4 57}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 12 + 4 57}{2 ( - 6 )}, x_{2} = \frac{- 12 - 4 57}{2 ( - 6 )}

x = \frac{- 12 + 4 57}{2 ( - 6 )} : - \frac{- 3 + 57}{3}

x = \frac{- 12 - 4 57}{2 ( - 6 )} : \frac{3 + 57}{3}

The solutions to the quadratic equation are:

x = - \frac{- 3 + 57}{3}, x = \frac{3 + 57}{3}

8 x^{2} + 9 x = 8

\frac{x - 4}{x + 6} < 1

21 \leq 3 + 9 x

112

(1 + \frac{0.04}{2})^{2} - 1

What are the solutions to the equation 4x-2x^2=-32/3 ?
The solutions to the equation 4x-2x^2=-32/3 are x=-(-3+sqrt(57))/3 ,x=(3+sqrt(57))/3
Find the zeros of 4x-2x^2=-32/3
The zeros of 4x-2x^2=-32/3 are x=-(-3+sqrt(57))/3 ,x=(3+sqrt(57))/3