-35-12y=y^2

Solution for -35-12y=y^2 equation:

-35-12y=y^2

We move all terms to the left:

-35-12y-(y^2)=0

determiningTheFunctionDomain
-y^2-12y-35=0

We add all the numbers together, and all the variables

-1y^2-12y-35=0

a = -1; b = -12; c = -35;
Δ = b2-4ac
Δ = -122-4·(-1)·(-35)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*-1}=\frac{10}{-2}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*-1}=\frac{14}{-2}
=-7
$