What are the solutions to the equation x(x-1)=-5x^2+2 ?

The solutions to the equation x(x-1)=-5x^2+2 are x= 2/3 ,x=-1/2

Find the zeros of x(x-1)=-5x^2+2

The zeros of x(x-1)=-5x^2+2 are x= 2/3 ,x=-1/2

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x (x - 1) = - 5 x^{2} + 2

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

Decimal Notation

x = 0.66666 \dots, x = - 0.5

Solution steps

x (x - 1) = - 5 x^{2} + 2

Expand

x (x - 1) : x^{2} - x

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

Move

2

to the left side

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

Move

5 x^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 6 ( - 2 )}{2 \cdot 6}

(- 1)^{2} - 4 \cdot 6 (- 2) = 7

x_{1, 2} = \frac{- ( - 1 ) \pm 7}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 7}{2 \cdot 6}, x_{2} = \frac{- ( - 1 ) - 7}{2 \cdot 6}

x = \frac{- ( - 1 ) + 7}{2 \cdot 6} : \frac{2}{3}

x = \frac{- ( - 1 ) - 7}{2 \cdot 6} : - \frac{1}{2}

The solutions to the quadratic equation are:

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

12 - \frac{33}{4}

a^{2} + 6 a - 27

\frac{- 7 π}{9} (\frac{π}{180})

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

q - 16 \leq 30

What are the solutions to the equation x(x-1)=-5x^2+2 ?
The solutions to the equation x(x-1)=-5x^2+2 are x= 2/3 ,x=-1/2
Find the zeros of x(x-1)=-5x^2+2
The zeros of x(x-1)=-5x^2+2 are x= 2/3 ,x=-1/2