1/10y=y+18

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

1/10y=y+18

We move all terms to the left:

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


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We get rid of parentheses

1/10y-y-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}
$