y=12-y^2-7y

Solution for y=12-y^2-7y equation:

y=12-y^2-7y

We move all terms to the left:

y-(12-y^2-7y)=0

We get rid of parentheses

y^2+7y+y-12=0

We add all the numbers together, and all the variables

y^2+8y-12=0

a = 1; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·1·(-12)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*1}=\frac{-8-4\sqrt{7}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*1}=\frac{-8+4\sqrt{7}}{2}
$