8+7/10y=6-1/5y

Solution for 8+7/10y=6-1/5y equation:

8+7/10y=6-1/5y

We move all terms to the left:

8+7/10y-(6-1/5y)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

7/10y-(-1/5y+6)+8=0

We get rid of parentheses

7/10y+1/5y-6+8=0

We calculate fractions


35y/50y^2+10y/50y^2-6+8=0

We add all the numbers together, and all the variables

35y/50y^2+10y/50y^2+2=0

We multiply all the terms by the denominator


35y+10y+2*50y^2=0

We add all the numbers together, and all the variables

45y+2*50y^2=0

Wy multiply elements

100y^2+45y=0

a = 100; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·100·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*100}=\frac{-90}{200}
=-9/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*100}=\frac{0}{200}
=0
$