y^2+48y+108=0

Solution for y^2+48y+108=0 equation:

y^2+48y+108=0

a = 1; b = 48; c = +108;
Δ = b2-4ac
Δ = 482-4·1·108
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{13}}{2*1}=\frac{-48-12\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{13}}{2*1}=\frac{-48+12\sqrt{13}}{2}
$