y^2-13y+12=6

Solution for y^2-13y+12=6 equation:

y^2-13y+12=6

We move all terms to the left:

y^2-13y+12-(6)=0

We add all the numbers together, and all the variables

y^2-13y+6=0

a = 1; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·1·6
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{145}}{2*1}=\frac{13-\sqrt{145}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{145}}{2*1}=\frac{13+\sqrt{145}}{2}
$