180=1/5y+y

Solution for 180=1/5y+y equation:

180=1/5y+y

We move all terms to the left:

180-(1/5y+y)=0


Domain of the equation: 5y+y)!=0

y∈R


We add all the numbers together, and all the variables

-(+y+1/5y)+180=0

We get rid of parentheses

-y-1/5y+180=0

We multiply all the terms by the denominator


-y*5y+180*5y-1=0

Wy multiply elements

-5y^2+900y-1=0

a = -5; b = 900; c = -1;
Δ = b2-4ac
Δ = 9002-4·(-5)·(-1)
Δ = 809980
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:

$\sqrt{\Delta}=\sqrt{809980}=\sqrt{4*202495}=\sqrt{4}*\sqrt{202495}=2\sqrt{202495}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-2\sqrt{202495}}{2*-5}=\frac{-900-2\sqrt{202495}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+2\sqrt{202495}}{2*-5}=\frac{-900+2\sqrt{202495}}{-10}
$