Y=x2+12x+11

Solution for Y=x2+12x+11 equation:

=Y2+12Y+11

We move all terms to the left:

-(Y2+12Y+11)=0

We add all the numbers together, and all the variables

-(+Y^2+12Y+11)=0

We get rid of parentheses

-Y^2-12Y-11=0

We add all the numbers together, and all the variables

-1Y^2-12Y-11=0

a = -1; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·(-1)·(-11)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10}{2*-1}=\frac{2}{-2}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10}{2*-1}=\frac{22}{-2}
=-11
$