What are the solutions to the equation 2000x^2+1000x=3000 ?

The solutions to the equation 2000x^2+1000x=3000 are x=1,x=-3/2

Find the zeros of 2000x^2+1000x=3000

The zeros of 2000x^2+1000x=3000 are x=1,x=-3/2

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2000 x^{2} + 1000 x = 3000

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

Decimal Notation

x = 1, x = - 1.5

Solution steps

2000 x^{2} + 1000 x = 3000

Move

3000

to the left side

2000 x^{2} + 1000 x - 3000 = 0

Divide both sides by

2000

\frac{2000 x ^{2}}{2000} + \frac{1000 x}{2000} - \frac{3000}{2000} = \frac{0}{2000}

Write in the standard form

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

x^{2} + \frac{1 \cdot x}{2} - \frac{3}{2} = 0

Solve with the quadratic formula

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

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

x_{1, 2} = \frac{- \frac{1}{2} \pm \frac{5}{2}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- \frac{1}{2} + \frac{5}{2}}{2 \cdot 1}, x_{2} = \frac{- \frac{1}{2} - \frac{5}{2}}{2 \cdot 1}

x = \frac{- \frac{1}{2} + \frac{5}{2}}{2 \cdot 1} : 1

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

The solutions to the quadratic equation are:

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

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

0 = - 16 x^{2} + 64 x + 48

4 (4 x - 3)^{2} - 10 = 26

x^{2} + 11 x + 50 = 20

4 x^{2} - 13 x = - 3

What are the solutions to the equation 2000x^2+1000x=3000 ?
The solutions to the equation 2000x^2+1000x=3000 are x=1,x=-3/2
Find the zeros of 2000x^2+1000x=3000
The zeros of 2000x^2+1000x=3000 are x=1,x=-3/2