20*3/5y+8y=500

Solution for 20*3/5y+8y=500 equation:

20*3/5y+8y=500

We move all terms to the left:

20*3/5y+8y-(500)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

8y+20*3/5y-500=0

We multiply all the terms by the denominator


8y*5y-500*5y+20*3=0

We add all the numbers together, and all the variables

8y*5y-500*5y+60=0

Wy multiply elements

40y^2-2500y+60=0

a = 40; b = -2500; c = +60;
Δ = b2-4ac
Δ = -25002-4·40·60
Δ = 6240400
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:

$\sqrt{\Delta}=\sqrt{6240400}=\sqrt{400*15601}=\sqrt{400}*\sqrt{15601}=20\sqrt{15601}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-20\sqrt{15601}}{2*40}=\frac{2500-20\sqrt{15601}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+20\sqrt{15601}}{2*40}=\frac{2500+20\sqrt{15601}}{80}
$