-9+27/18y-10y=12

Solution for -9+27/18y-10y=12 equation:

-9+27/18y-10y=12

We move all terms to the left:

-9+27/18y-10y-(12)=0


Domain of the equation: 18y!=0

y!=0/18

y!=0

y∈R


We add all the numbers together, and all the variables

-10y+27/18y-21=0

We multiply all the terms by the denominator


-10y*18y-21*18y+27=0

Wy multiply elements

-180y^2-378y+27=0

a = -180; b = -378; c = +27;
Δ = b2-4ac
Δ = -3782-4·(-180)·27
Δ = 162324
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:

$\sqrt{\Delta}=\sqrt{162324}=\sqrt{324*501}=\sqrt{324}*\sqrt{501}=18\sqrt{501}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-18\sqrt{501}}{2*-180}=\frac{378-18\sqrt{501}}{-360}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+18\sqrt{501}}{2*-180}=\frac{378+18\sqrt{501}}{-360}
$