5*(40-0.4y)2y=200

Solution for 5*(40-0.4y)2y=200 equation:

5(40-0.4y)2y=200

We move all terms to the left:

5(40-0.4y)2y-(200)=0

We add all the numbers together, and all the variables

5(-0.4y+40)2y-200=0

We multiply parentheses

0y^2+400y-200=0

We add all the numbers together, and all the variables

y^2+400y-200=0

a = 1; b = 400; c = -200;
Δ = b2-4ac
Δ = 4002-4·1·(-200)
Δ = 160800
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:

$\sqrt{\Delta}=\sqrt{160800}=\sqrt{400*402}=\sqrt{400}*\sqrt{402}=20\sqrt{402}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-20\sqrt{402}}{2*1}=\frac{-400-20\sqrt{402}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+20\sqrt{402}}{2*1}=\frac{-400+20\sqrt{402}}{2}
$