a^2-48a+288=0

Solution for a^2-48a+288=0 equation:

a^2-48a+288=0

a = 1; b = -48; c = +288;
Δ = b2-4ac
Δ = -482-4·1·288
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{2}}{2*1}=\frac{48-24\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{2}}{2*1}=\frac{48+24\sqrt{2}}{2}
$