x-1/5x=1600

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

x-1/5x=1600

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


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}
$