-1/2y-2/5=1/5y+5

Solution for -1/2y-2/5=1/5y+5 equation:

-1/2y-2/5=1/5y+5

We move all terms to the left:

-1/2y-2/5-(1/5y+5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

-1/2y-1/5y-5-2/5=0

We calculate fractions


(-125y)/250y^2+(-2y)/250y^2+(-4y)/250y^2-5=0

We multiply all the terms by the denominator


(-125y)+(-2y)+(-4y)-5*250y^2=0

Wy multiply elements

-1250y^2+(-125y)+(-2y)+(-4y)=0

We get rid of parentheses

-1250y^2-125y-2y-4y=0

We add all the numbers together, and all the variables

-1250y^2-131y=0

a = -1250; b = -131; c = 0;
Δ = b2-4ac
Δ = -1312-4·(-1250)·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-131)-131}{2*-1250}=\frac{0}{-2500}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131)+131}{2*-1250}=\frac{262}{-2500}
=-131/1250
$