x^2+24x+54=0

Solution for x^2+24x+54=0 equation:

x^2+24x+54=0

a = 1; b = 24; c = +54;
Δ = b2-4ac
Δ = 242-4·1·54
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{10}}{2*1}=\frac{-24-6\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{10}}{2*1}=\frac{-24+6\sqrt{10}}{2}
$