400x-3000/400x=0.30

Solution for 400x-3000/400x=0.30 equation:

400x-3000/400x=0.30

We move all terms to the left:

400x-3000/400x-(0.30)=0


Domain of the equation: 400x!=0

x!=0/400

x!=0

x∈R


We add all the numbers together, and all the variables

400x-3000/400x-(0.3)=0

We add all the numbers together, and all the variables

400x-3000/400x-0.3=0

We multiply all the terms by the denominator


400x*400x-(0.3)*400x-3000=0

We multiply parentheses

400x*400x-120x-3000=0

Wy multiply elements

160000x^2-120x-3000=0

a = 160000; b = -120; c = -3000;
Δ = b2-4ac
Δ = -1202-4·160000·(-3000)
Δ = 1920014400
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:

$\sqrt{\Delta}=\sqrt{1920014400}=\sqrt{1600*1200009}=\sqrt{1600}*\sqrt{1200009}=40\sqrt{1200009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-40\sqrt{1200009}}{2*160000}=\frac{120-40\sqrt{1200009}}{320000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+40\sqrt{1200009}}{2*160000}=\frac{120+40\sqrt{1200009}}{320000}
$