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

The solutions to the equation x^2-x= 1/3 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

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

The zeros of x^2-x= 1/3 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

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x^{2} - x = \frac{1}{3}

x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

Decimal Notation

x = 1.26376 \dots, x = - 0.26376 \dots

Solution steps

x^{2} - x = \frac{1}{3}

Multiply both sides by

3

3 x^{2} - 3 x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 3 (- 1) = 21

x_{1, 2} = \frac{- ( - 3 ) \pm 21}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 21}{2 \cdot 3}, x_{2} = \frac{- ( - 3 ) - 21}{2 \cdot 3}

x = \frac{- ( - 3 ) + 21}{2 \cdot 3} : \frac{3 + 21}{6}

x = \frac{- ( - 3 ) - 21}{2 \cdot 3} : \frac{3 - 21}{6}

The solutions to the quadratic equation are:

x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

x^{2} + 2 x + 7 = 15

x, 0 = - 0.02 x^{2} + x + 2.6

(2 x - 7)^{2} + 3 = 52

3 x^{2} - 5 x = 2 x + 6

5 x^{2} - 8 x + 10 = 0

What are the solutions to the equation x^2-x= 1/3 ?
The solutions to the equation x^2-x= 1/3 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6
Find the zeros of x^2-x= 1/3
The zeros of x^2-x= 1/3 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6