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

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

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

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

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2 x^{2} + 1 = 3 x

x = 1, x = \frac{1}{2}

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 \cdot 1}{2 \cdot 2}

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 1, x = \frac{1}{2}

2 x^{2} - 24 x + 144 = 0

- 12 w^{2} = 7 + 6 w

96 = 80 t - 16 t^{2}

x^{2} + 4 x + 4 = 0

8^{2} = 5^{2} + x^{2}

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