3/5*x=2000

Solution for 3/5*x=2000 equation:

3/5*x=2000

We move all terms to the left:

3/5*x-(2000)=0


Domain of the equation: 5*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-2000*5*x+3=0

Wy multiply elements

-10000x*x+3=0

Wy multiply elements

-10000x^2+3=0

a = -10000; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-10000)·3
Δ = 120000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120000}=\sqrt{40000*3}=\sqrt{40000}*\sqrt{3}=200\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{3}}{2*-10000}=\frac{0-200\sqrt{3}}{-20000}
=-\frac{200\sqrt{3}}{-20000}
=-\frac{\sqrt{3}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{3}}{2*-10000}=\frac{0+200\sqrt{3}}{-20000}
=\frac{200\sqrt{3}}{-20000}
=\frac{\sqrt{3}}{-100}
$