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

The solutions to the equation 2x^2-1=3x are x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4

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

The zeros of 2x^2-1=3x are x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4

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2 x^{2} - 1 = 3 x

x = \frac{3 + 17}{4}, x = \frac{3 - 17}{4}

Solution steps

2 x^{2} - 1 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 2 (- 1) = 17

x_{1, 2} = \frac{- ( - 3 ) \pm 17}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 17}{2 \cdot 2}, x_{2} = \frac{- ( - 3 ) - 17}{2 \cdot 2}

x = \frac{- ( - 3 ) + 17}{2 \cdot 2} : \frac{3 + 17}{4}

x = \frac{- ( - 3 ) - 17}{2 \cdot 2} : \frac{3 - 17}{4}

The solutions to the quadratic equation are:

x = \frac{3 + 17}{4}, x = \frac{3 - 17}{4}

8 x^{2} + 2 (x + 6) = 12

x^{2} + 22 x + 117 = 0

a, y^{2} + a^{2} = (a + y) 2 - a (a + 1)

x^{2} + 2 x = 15

x^{2} + 8 x - 30 = 18

What are the solutions to the equation 2x^2-1=3x ?
The solutions to the equation 2x^2-1=3x are x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4
Find the zeros of 2x^2-1=3x
The zeros of 2x^2-1=3x are x=(3+sqrt(17))/4 ,x=(3-sqrt(17))/4