What are the solutions to the equation 50=(3x(20-x))/2 ?

The solutions to the equation 50=(3x(20-x))/2 are x=(10(3-sqrt(6)))/3 ,x=(10(3+sqrt(6)))/3

Find the zeros of 50=(3x(20-x))/2

The zeros of 50=(3x(20-x))/2 are x=(10(3-sqrt(6)))/3 ,x=(10(3+sqrt(6)))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

50 = \frac{3 x ( 20 - x )}{2}

x = \frac{10 ( 3 - 6 )}{3}, x = \frac{10 ( 3 + 6 )}{3}

Decimal Notation

x = 1.83503 \dots, x = 18.16496 \dots

Solution steps

50 = \frac{3 x ( 20 - x )}{2}

Multiply both sides by

2

100 = 3 x (20 - x)

Expand

3 x (20 - x) : 60 x - 3 x^{2}

100 = 60 x - 3 x^{2}

Switch sides

60 x - 3 x^{2} = 100

Move

100

to the left side

60 x - 3 x^{2} - 100 = 0

Write in the standard form

a x^{2} + b x + c = 0

- 3 x^{2} + 60 x - 100 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 60 \pm 6 0 ^{2} - 4 ( - 3 ) ( - 100 )}{2 ( - 3 )}

6 0^{2} - 4 (- 3) (- 100) = 206

x_{1, 2} = \frac{- 60 \pm 20 6}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 60 + 20 6}{2 ( - 3 )}, x_{2} = \frac{- 60 - 20 6}{2 ( - 3 )}

x = \frac{- 60 + 20 6}{2 ( - 3 )} : \frac{10 ( 3 - 6 )}{3}

x = \frac{- 60 - 20 6}{2 ( - 3 )} : \frac{10 ( 3 + 6 )}{3}

The solutions to the quadratic equation are:

x = \frac{10 ( 3 - 6 )}{3}, x = \frac{10 ( 3 + 6 )}{3}

4 x^{2} + 36 x + 31

15 x^{2} - 6 = - 13 x

x, x^{2} + 9 b^{2} = 0

4 x (2 x - 1) - x = 3

2 x^{2} + 4 x - 1

What are the solutions to the equation 50=(3x(20-x))/2 ?
The solutions to the equation 50=(3x(20-x))/2 are x=(10(3-sqrt(6)))/3 ,x=(10(3+sqrt(6)))/3
Find the zeros of 50=(3x(20-x))/2
The zeros of 50=(3x(20-x))/2 are x=(10(3-sqrt(6)))/3 ,x=(10(3+sqrt(6)))/3