y-18/y=12

Solution for y-18/y=12 equation:

y-18/y=12

We move all terms to the left:

y-18/y-(12)=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


y*y-12*y-18=0

We add all the numbers together, and all the variables

-12y+y*y-18=0

Wy multiply elements

y^2-12y-18=0

a = 1; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·1·(-18)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{6}}{2*1}=\frac{12-6\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{6}}{2*1}=\frac{12+6\sqrt{6}}{2}
$