1/5y+9=1/2y+18

Solution for 1/5y+9=1/2y+18 equation:

1/5y+9=1/2y+18

We move all terms to the left:

1/5y+9-(1/2y+18)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y+18)!=0

y∈R


We get rid of parentheses

1/5y-1/2y-18+9=0

We calculate fractions


2y/10y^2+(-5y)/10y^2-18+9=0

We add all the numbers together, and all the variables

2y/10y^2+(-5y)/10y^2-9=0

We multiply all the terms by the denominator


2y+(-5y)-9*10y^2=0

Wy multiply elements

-90y^2+2y+(-5y)=0

We get rid of parentheses

-90y^2+2y-5y=0

We add all the numbers together, and all the variables

-90y^2-3y=0

a = -90; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-90)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-90}=\frac{0}{-180}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-90}=\frac{6}{-180}
=-1/30
$