y2-12y=13

Solution for y2-12y=13 equation:

y2-12y=13

We move all terms to the left:

y2-12y-(13)=0

We add all the numbers together, and all the variables

y^2-12y-13=0

a = 1; b = -12; c = -13;
Δ = b2-4ac
Δ = -122-4·1·(-13)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-14}{2*1}=\frac{-2}{2}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+14}{2*1}=\frac{26}{2}
=13
$