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

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

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

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

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

x = - \frac{5}{3}, x = 1

Decimal Notation

x = - 1.66666 \dots, x = 1

Solution steps

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

Expand

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

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

Move

5 x^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 ( - 3 ) \cdot 5}{2 ( - 3 )}

(- 2)^{2} - 4 (- 3) \cdot 5 = 8

x_{1, 2} = \frac{- ( - 2 ) \pm 8}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 8}{2 ( - 3 )}, x_{2} = \frac{- ( - 2 ) - 8}{2 ( - 3 )}

x = \frac{- ( - 2 ) + 8}{2 ( - 3 )} : - \frac{5}{3}

x = \frac{- ( - 2 ) - 8}{2 ( - 3 )} : 1

The solutions to the quadratic equation are:

x = - \frac{5}{3}, x = 1

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

20 x^{2} - 7 x - 3 = 0

50 x^{2} = 18

x, z = 3 x^{2} - 12 x + 2 y^{3} + 3 y^{2} - 12 y

0 = 18 x^{2} - 18 x - 108

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