x=500,000/3,200,000

Solution for x=500,000/3,200,000 equation:

x=500.000/3.200.000

We move all terms to the left:

x-(500.000/3.200.000)=0

We add all the numbers together, and all the variables

x-(+500.000/3.200.000)=0

We get rid of parentheses

x-500.000/3.200.000=0

We multiply all the terms by the denominator


x*3.200.000-500.000=0

We add all the numbers together, and all the variables

x*3.200.000-500=0

Wy multiply elements

3x^2-500=0

a = 3; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·3·(-500)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{15}}{2*3}=\frac{0-20\sqrt{15}}{6}
=-\frac{20\sqrt{15}}{6}
=-\frac{10\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{15}}{2*3}=\frac{0+20\sqrt{15}}{6}
=\frac{20\sqrt{15}}{6}
=\frac{10\sqrt{15}}{3}
$