What are the solutions to the equation 3x^2-1=4x ?

The solutions to the equation 3x^2-1=4x are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3

Find the zeros of 3x^2-1=4x

The zeros of 3x^2-1=4x are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3

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3 x^{2} - 1 = 4 x

x = \frac{2 + 7}{3}, x = \frac{2 - 7}{3}

Decimal Notation

x = 1.54858 \dots, x = - 0.21525 \dots

Solution steps

3 x^{2} - 1 = 4 x

Move

4 x

to the left side

3 x^{2} - 1 - 4 x = 0

Write in the standard form

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

3 x^{2} - 4 x - 1 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 3 (- 1) = 27

x_{1, 2} = \frac{- ( - 4 ) \pm 2 7}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 7}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 7}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 7}{2 \cdot 3} : \frac{2 + 7}{3}

x = \frac{- ( - 4 ) - 2 7}{2 \cdot 3} : \frac{2 - 7}{3}

The solutions to the quadratic equation are:

x = \frac{2 + 7}{3}, x = \frac{2 - 7}{3}

(5 - 3 y)^{2} + y^{2} = 25

3 n^{2} - n - 6 = 0

s^{2} - s = 0

16.7 - \frac{20 x ^{2}}{10} = 0

- x^{2} + 10 x + 25 = 0

What are the solutions to the equation 3x^2-1=4x ?
The solutions to the equation 3x^2-1=4x are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3
Find the zeros of 3x^2-1=4x
The zeros of 3x^2-1=4x are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3