y^2-6y=12

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

y^2-6y=12

We move all terms to the left:

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

a = 1; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·1·(-12)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*1}=\frac{6-2\sqrt{21}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*1}=\frac{6+2\sqrt{21}}{2}
$