1/5x=x-1600

Solution for 1/5x=x-1600 equation:

1/5x=x-1600

We move all terms to the left:

1/5x-(x-1600)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+1600=0

We multiply all the terms by the denominator


-x*5x+1600*5x+1=0

Wy multiply elements

-5x^2+8000x+1=0

a = -5; b = 8000; c = +1;
Δ = b2-4ac
Δ = 80002-4·(-5)·1
Δ = 64000020
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:

$\sqrt{\Delta}=\sqrt{64000020}=\sqrt{4*16000005}=\sqrt{4}*\sqrt{16000005}=2\sqrt{16000005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8000)-2\sqrt{16000005}}{2*-5}=\frac{-8000-2\sqrt{16000005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8000)+2\sqrt{16000005}}{2*-5}=\frac{-8000+2\sqrt{16000005}}{-10}
$