1/2x+200=7/10x

Solution for 1/2x+200=7/10x equation:

1/2x+200=7/10x

We move all terms to the left:

1/2x+200-(7/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+7/10x)+200=0

We get rid of parentheses

1/2x-7/10x+200=0

We calculate fractions


10x/20x^2+(-14x)/20x^2+200=0

We multiply all the terms by the denominator


10x+(-14x)+200*20x^2=0

Wy multiply elements

4000x^2+10x+(-14x)=0

We get rid of parentheses

4000x^2+10x-14x=0

We add all the numbers together, and all the variables

4000x^2-4x=0

a = 4000; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·4000·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*4000}=\frac{0}{8000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*4000}=\frac{8}{8000}
=1/1000
$