-3/y+5=5/2y+10+2

Solution for -3/y+5=5/2y+10+2 equation:

-3/y+5=5/2y+10+2

We move all terms to the left:

-3/y+5-(5/2y+10+2)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y+10+2)!=0

We move all terms containing y to the left, all other terms to the right

2y+2)!=-10

y∈R


We add all the numbers together, and all the variables

-3/y-(5/2y+12)+5=0

We get rid of parentheses

-3/y-5/2y-12+5=0

We calculate fractions


(-6y)/2y^2+(-5y)/2y^2-12+5=0

We add all the numbers together, and all the variables

(-6y)/2y^2+(-5y)/2y^2-7=0

We multiply all the terms by the denominator


(-6y)+(-5y)-7*2y^2=0

Wy multiply elements

-14y^2+(-6y)+(-5y)=0

We get rid of parentheses

-14y^2-6y-5y=0

We add all the numbers together, and all the variables

-14y^2-11y=0

a = -14; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-14)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-14}=\frac{0}{-28}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-14}=\frac{22}{-28}
=-11/14
$