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

The solutions to the equation -3+4x^2-2x=4x are x=(3+sqrt(21))/4 ,x=(3-sqrt(21))/4

Find the zeros of -3+4x^2-2x=4x

The zeros of -3+4x^2-2x=4x are x=(3+sqrt(21))/4 ,x=(3-sqrt(21))/4

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

x = \frac{3 + 21}{4}, x = \frac{3 - 21}{4}

Decimal Notation

x = 1.89564 \dots, x = - 0.39564 \dots

Solution steps

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

Move

4 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 4 (- 3) = 221

x_{1, 2} = \frac{- ( - 6 ) \pm 2 21}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 21}{2 \cdot 4}, x_{2} = \frac{- ( - 6 ) - 2 21}{2 \cdot 4}

x = \frac{- ( - 6 ) + 2 21}{2 \cdot 4} : \frac{3 + 21}{4}

x = \frac{- ( - 6 ) - 2 21}{2 \cdot 4} : \frac{3 - 21}{4}

The solutions to the quadratic equation are:

x = \frac{3 + 21}{4}, x = \frac{3 - 21}{4}

x^{2} + 1 6^{2} = 2 0^{2}

(x - 3) (4 + 3) - x^{2} - \frac{5}{4} = (x - \frac{x}{5}) - (3 x - \frac{3}{4})

x^{2} + \frac{3}{2} x + 1 = 0

m^{2} + 8 m + 12 = 0

3 x^{2} - 6 x + 4

What are the solutions to the equation -3+4x^2-2x=4x ?
The solutions to the equation -3+4x^2-2x=4x are x=(3+sqrt(21))/4 ,x=(3-sqrt(21))/4
Find the zeros of -3+4x^2-2x=4x
The zeros of -3+4x^2-2x=4x are x=(3+sqrt(21))/4 ,x=(3-sqrt(21))/4