y^2-8y=39

Solution for y^2-8y=39 equation:

y^2-8y=39

We move all terms to the left:

y^2-8y-(39)=0

a = 1; b = -8; c = -39;
Δ = b2-4ac
Δ = -82-4·1·(-39)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{55}}{2*1}=\frac{8-2\sqrt{55}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{55}}{2*1}=\frac{8+2\sqrt{55}}{2}
$