y-1/5y=6400

Solution for y-1/5y=6400 equation:

y-1/5y=6400

We move all terms to the left:

y-1/5y-(6400)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


y*5y-6400*5y-1=0

Wy multiply elements

5y^2-32000y-1=0

a = 5; b = -32000; c = -1;
Δ = b2-4ac
Δ = -320002-4·5·(-1)
Δ = 1024000020
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1024000020}=\sqrt{36*28444445}=\sqrt{36}*\sqrt{28444445}=6\sqrt{28444445}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32000)-6\sqrt{28444445}}{2*5}=\frac{32000-6\sqrt{28444445}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32000)+6\sqrt{28444445}}{2*5}=\frac{32000+6\sqrt{28444445}}{10}
$