(3x)/x=x/400

Solution for (3x)/x=x/400 equation:

(3x)/x=x/400

We move all terms to the left:

(3x)/x-(x/400)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x/x-(+x/400)=0

We get rid of parentheses

3x/x-x/400=0

We calculate fractions


(-1x^2)/400x+1200x/400x=0

We multiply all the terms by the denominator


(-1x^2)+1200x=0

We get rid of parentheses

-1x^2+1200x=0

a = -1; b = 1200; c = 0;
Δ = b2-4ac
Δ = 12002-4·(-1)·0
Δ = 1440000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1440000}=1200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-1200}{2*-1}=\frac{-2400}{-2}
=+1200
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+1200}{2*-1}=\frac{0}{-2}
=0
$