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

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

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

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

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3 x = x^{2} - 2

x = \frac{3 + 17}{2}, x = \frac{3 - 17}{2}

Decimal Notation

x = 3.56155 \dots, x = - 0.56155 \dots

Solution steps

3 x = x^{2} - 2

Switch sides

x^{2} - 2 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

x = \frac{- ( - 3 ) + 17}{2 \cdot 1} : \frac{3 + 17}{2}

x = \frac{- ( - 3 ) - 17}{2 \cdot 1} : \frac{3 - 17}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 17}{2}, x = \frac{3 - 17}{2}

9 x^{2} + 6 x = - 10

(x - 1) (3 x + 2) = 0

(11 x - 12)^{2} = 20

8 - (x + 4)^{2} = 4 - (0.5 x + 1.8)^{2}

(2 x) x - 1 = 4

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