18+y=1/10y

Solution for 18+y=1/10y equation:

18+y=1/10y

We move all terms to the left:

18+y-(1/10y)=0


Domain of the equation: 10y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+1/10y)+18=0

We get rid of parentheses

y-1/10y+18=0

We multiply all the terms by the denominator


y*10y+18*10y-1=0

Wy multiply elements

10y^2+180y-1=0

a = 10; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·10·(-1)
Δ = 32440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8110}}{2*10}=\frac{-180-2\sqrt{8110}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8110}}{2*10}=\frac{-180+2\sqrt{8110}}{20}
$