What are the solutions to the equation (5-x)/(6000)= 1/2*0.001*(x-1)^2 ?

The solutions to the equation (5-x)/(6000)= 1/2*0.001*(x-1)^2 are x=2,x=-1/3

Find the zeros of (5-x)/(6000)= 1/2*0.001*(x-1)^2

The zeros of (5-x)/(6000)= 1/2*0.001*(x-1)^2 are x=2,x=-1/3

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\frac{5 - x}{6000} = \frac{1}{2} \cdot 0.001 \cdot (x - 1)^{2}

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

Decimal Notation

x = 2, x = - 0.33333 \dots

Solution steps

\frac{5 - x}{6000} = \frac{1}{2} \cdot 0.001 (x - 1)^{2}

Find Least Common Multiplier of

6000, 2 : 6000

Multiply by LCM=

6000

\frac{5 - x}{6000} \cdot 6000 = \frac{1}{2} \cdot 0.001 (x - 1)^{2} \cdot 6000

Simplify

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

Expand

3 (x - 1)^{2} : 3 x^{2} - 6 x + 3

5 - x = 3 x^{2} - 6 x + 3

Switch sides

3 x^{2} - 6 x + 3 = 5 - x

Move

x

to the left side

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

Move

5

to the left side

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

Solve with the quadratic formula

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

(- 5)^{2} - 4 \cdot 3 (- 2) = 7

x_{1, 2} = \frac{- ( - 5 ) \pm 7}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 7}{2 \cdot 3}, x_{2} = \frac{- ( - 5 ) - 7}{2 \cdot 3}

x = \frac{- ( - 5 ) + 7}{2 \cdot 3} : 2

x = \frac{- ( - 5 ) - 7}{2 \cdot 3} : - \frac{1}{3}

The solutions to the quadratic equation are:

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

2 x^{2} + 11 = x^{2} + 12

\frac{1}{3} x^{2} - \frac{123}{4} x + \frac{1}{6} = 0

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

3 m^{2} + 7 m + 2 = 0

(x - 3) (x + 5) + 6 = 2 x + 7

What are the solutions to the equation (5-x)/(6000)= 1/2*0.001*(x-1)^2 ?
The solutions to the equation (5-x)/(6000)= 1/2*0.001*(x-1)^2 are x=2,x=-1/3
Find the zeros of (5-x)/(6000)= 1/2*0.001*(x-1)^2
The zeros of (5-x)/(6000)= 1/2*0.001*(x-1)^2 are x=2,x=-1/3