0=y^2-12y-11

Solution for 0=y^2-12y-11 equation:

0=y^2-12y-11

We move all terms to the left:

0-(y^2-12y-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 = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{47}}{2*-1}=\frac{-12-2\sqrt{47}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{47}}{2*-1}=\frac{-12+2\sqrt{47}}{-2}
$