y/5y-9=8-2y

Solution for y/5y-9=8-2y equation:

y/5y-9=8-2y

We move all terms to the left:

y/5y-9-(8-2y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y/5y-(-2y+8)-9=0

We get rid of parentheses

y/5y+2y-8-9=0

We multiply all the terms by the denominator


y+2y*5y-8*5y-9*5y=0

Wy multiply elements

10y^2+y-40y-45y=0

We add all the numbers together, and all the variables

10y^2-84y=0

a = 10; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·10·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*10}=\frac{0}{20}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*10}=\frac{168}{20}
=8+2/5
$