3/5y+y=8000

Solution for 3/5y+y=8000 equation:

3/5y+y=8000

We move all terms to the left:

3/5y+y-(8000)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y+3/5y-8000=0

We multiply all the terms by the denominator


y*5y-8000*5y+3=0

Wy multiply elements

5y^2-40000y+3=0

a = 5; b = -40000; c = +3;
Δ = b2-4ac
Δ = -400002-4·5·3
Δ = 1599999940
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:

$\sqrt{\Delta}=\sqrt{1599999940}=\sqrt{23716*67465}=\sqrt{23716}*\sqrt{67465}=154\sqrt{67465}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40000)-154\sqrt{67465}}{2*5}=\frac{40000-154\sqrt{67465}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40000)+154\sqrt{67465}}{2*5}=\frac{40000+154\sqrt{67465}}{10}
$