y^2-6y=39

Solution for y^2-6y=39 equation:

y^2-6y=39

We move all terms to the left:

y^2-6y-(39)=0

a = 1; b = -6; c = -39;
Δ = b2-4ac
Δ = -62-4·1·(-39)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{3}}{2*1}=\frac{6-8\sqrt{3}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{3}}{2*1}=\frac{6+8\sqrt{3}}{2}
$