1000-1/4x=-200+1/2x

Solution for 1000-1/4x=-200+1/2x equation:

1000-1/4x=-200+1/2x

We move all terms to the left:

1000-1/4x-(-200+1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(1/2x-200)+1000=0

We get rid of parentheses

-1/4x-1/2x+200+1000=0

We calculate fractions


(-2x)/8x^2+(-4x)/8x^2+200+1000=0

We add all the numbers together, and all the variables

(-2x)/8x^2+(-4x)/8x^2+1200=0

We multiply all the terms by the denominator


(-2x)+(-4x)+1200*8x^2=0

Wy multiply elements

9600x^2+(-2x)+(-4x)=0

We get rid of parentheses

9600x^2-2x-4x=0

We add all the numbers together, and all the variables

9600x^2-6x=0

a = 9600; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·9600·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*9600}=\frac{0}{19200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*9600}=\frac{12}{19200}
=1/1600
$