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

The solutions to the equation 3x^2-1=2x are x=1,x=-1/3

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

The zeros of 3x^2-1=2x are x=1,x=-1/3

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3 x^{2} - 1 = 2 x

x = 1, x = - \frac{1}{3}

Decimal Notation

x = 1, x = - 0.33333 \dots

Solution steps

3 x^{2} - 1 = 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

x = \frac{- ( - 2 ) + 4}{2 \cdot 3} : 1

x = \frac{- ( - 2 ) - 4}{2 \cdot 3} : - \frac{1}{3}

The solutions to the quadratic equation are:

x = 1, x = - \frac{1}{3}

(1.16 \cdot 1 0^{2}) \cdot (0.8571 - x) (0.5714 - x) - 2 x^{2} = 0

2 y^{(2)} - 9 y + 1 = 0

8.5076 x^{2} + (- 452.881) x + 4293.054 = 0

4 a^{2} - 10 a - 24 = 0

x^{2} - 7 x = 0

What are the solutions to the equation 3x^2-1=2x ?
The solutions to the equation 3x^2-1=2x are x=1,x=-1/3
Find the zeros of 3x^2-1=2x
The zeros of 3x^2-1=2x are x=1,x=-1/3