X^2-48x+468=0

Solution for X^2-48x+468=0 equation:

X^2-48X+468=0

a = 1; b = -48; c = +468;
Δ = b2-4ac
Δ = -482-4·1·468
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{3}}{2*1}=\frac{48-12\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{3}}{2*1}=\frac{48+12\sqrt{3}}{2}
$