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

The solutions to the equation x^2-x= 3/2 are x=(1+sqrt(7))/2 ,x=(1-sqrt(7))/2

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

The zeros of x^2-x= 3/2 are x=(1+sqrt(7))/2 ,x=(1-sqrt(7))/2

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

x = \frac{1 + 7}{2}, x = \frac{1 - 7}{2}

Decimal Notation

x = 1.82287 \dots, x = - 0.82287 \dots

Solution steps

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

Multiply both sides by

2

2 x^{2} - 2 x = 3

Move

3

to the left side

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

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 2 (- 3) = 27

x_{1, 2} = \frac{- ( - 2 ) \pm 2 7}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 7}{2 \cdot 2}, x_{2} = \frac{- ( - 2 ) - 2 7}{2 \cdot 2}

x = \frac{- ( - 2 ) + 2 7}{2 \cdot 2} : \frac{1 + 7}{2}

x = \frac{- ( - 2 ) - 2 7}{2 \cdot 2} : \frac{1 - 7}{2}

The solutions to the quadratic equation are:

x = \frac{1 + 7}{2}, x = \frac{1 - 7}{2}

- x^{2} - 20 x - 100 = 0

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

x (x - 2) = 4

x^{2} - 2 x - 18 = 0

0.75 x^{2} - 6 x + 20 = 2.75 x + 1.5

What are the solutions to the equation x^2-x= 3/2 ?
The solutions to the equation x^2-x= 3/2 are x=(1+sqrt(7))/2 ,x=(1-sqrt(7))/2
Find the zeros of x^2-x= 3/2
The zeros of x^2-x= 3/2 are x=(1+sqrt(7))/2 ,x=(1-sqrt(7))/2