y^2-218y-27=0

Solution for y^2-218y-27=0 equation:

y^2-218y-27=0

a = 1; b = -218; c = -27;
Δ = b2-4ac
Δ = -2182-4·1·(-27)
Δ = 47632
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:

$\sqrt{\Delta}=\sqrt{47632}=\sqrt{16*2977}=\sqrt{16}*\sqrt{2977}=4\sqrt{2977}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-4\sqrt{2977}}{2*1}=\frac{218-4\sqrt{2977}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+4\sqrt{2977}}{2*1}=\frac{218+4\sqrt{2977}}{2}
$