2/5y+8=-1/2y+6

Solution for 2/5y+8=-1/2y+6 equation:

2/5y+8=-1/2y+6

We move all terms to the left:

2/5y+8-(-1/2y+6)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y+6)!=0

y∈R


We get rid of parentheses

2/5y+1/2y-6+8=0

We calculate fractions


4y/10y^2+5y/10y^2-6+8=0

We add all the numbers together, and all the variables

4y/10y^2+5y/10y^2+2=0

We multiply all the terms by the denominator


4y+5y+2*10y^2=0

We add all the numbers together, and all the variables

9y+2*10y^2=0

Wy multiply elements

20y^2+9y=0

a = 20; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·20·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*20}=\frac{-18}{40}
=-9/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*20}=\frac{0}{40}
=0
$