Y=x2+8x+12

Solution for Y=x2+8x+12 equation:

=Y2+8Y+12

We move all terms to the left:

-(Y2+8Y+12)=0

We add all the numbers together, and all the variables

-(+Y^2+8Y+12)=0

We get rid of parentheses

-Y^2-8Y-12=0

We add all the numbers together, and all the variables

-1Y^2-8Y-12=0

a = -1; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·(-1)·(-12)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*-1}=\frac{4}{-2}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*-1}=\frac{12}{-2}
=-6
$