What are the solutions to the equation 5x(x-2)-3x= 8/3 ?

The solutions to the equation 5x(x-2)-3x= 8/3 are x=(39+sqrt(2001))/(30),x=(39-sqrt(2001))/(30)

Find the zeros of 5x(x-2)-3x= 8/3

The zeros of 5x(x-2)-3x= 8/3 are x=(39+sqrt(2001))/(30),x=(39-sqrt(2001))/(30)

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

x = \frac{39 + 2001}{30}, x = \frac{39 - 2001}{30}

Decimal Notation

x = 2.79108 \dots, x = - 0.19108 \dots

Solution steps

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

Multiply both sides by

3

15 x (x - 2) - 9 x = 8

Expand

15 x (x - 2) - 9 x : 15 x^{2} - 39 x

15 x^{2} - 39 x = 8

Move

8

to the left side

15 x^{2} - 39 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 39 ) \pm ( - 39 ) ^{2} - 4 \cdot 15 ( - 8 )}{2 \cdot 15}

(- 39)^{2} - 4 \cdot 15 (- 8) = 2001

x_{1, 2} = \frac{- ( - 39 ) \pm 2001}{2 \cdot 15}

Separate the solutions

x_{1} = \frac{- ( - 39 ) + 2001}{2 \cdot 15}, x_{2} = \frac{- ( - 39 ) - 2001}{2 \cdot 15}

x = \frac{- ( - 39 ) + 2001}{2 \cdot 15} : \frac{39 + 2001}{30}

x = \frac{- ( - 39 ) - 2001}{2 \cdot 15} : \frac{39 - 2001}{30}

The solutions to the quadratic equation are:

x = \frac{39 + 2001}{30}, x = \frac{39 - 2001}{30}

(x + 3)^{2} = - x - 1

x^{2} - 2 x = - 7

3 x^{2} + 2 x - 8 = x^{2} + 2 (x - 2)

x^{2} - \frac{1}{25} = 0

0 = - 2 x^{2} + 9 x - 12

What are the solutions to the equation 5x(x-2)-3x= 8/3 ?
The solutions to the equation 5x(x-2)-3x= 8/3 are x=(39+sqrt(2001))/(30),x=(39-sqrt(2001))/(30)
Find the zeros of 5x(x-2)-3x= 8/3
The zeros of 5x(x-2)-3x= 8/3 are x=(39+sqrt(2001))/(30),x=(39-sqrt(2001))/(30)