y/10y+5=25+5y

Solution for y/10y+5=25+5y equation:

y/10y+5=25+5y

We move all terms to the left:

y/10y+5-(25+5y)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We add all the numbers together, and all the variables

y/10y-(5y+25)+5=0

We get rid of parentheses

y/10y-5y-25+5=0

We multiply all the terms by the denominator


y-5y*10y-25*10y+5*10y=0

Wy multiply elements

-50y^2+y-250y+50y=0

We add all the numbers together, and all the variables

-50y^2-199y=0

a = -50; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·(-50)·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-199}{2*-50}=\frac{0}{-100}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*-50}=\frac{398}{-100}
=-3+49/50
$