y^2=1-12y

Solution for y^2=1-12y equation:

y^2=1-12y

We move all terms to the left:

y^2-(1-12y)=0

We add all the numbers together, and all the variables

y^2-(-12y+1)=0

We get rid of parentheses

y^2+12y-1=0

a = 1; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·1·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{37}}{2*1}=\frac{-12-2\sqrt{37}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{37}}{2*1}=\frac{-12+2\sqrt{37}}{2}
$