X^2+24x+138=0

Solution for X^2+24x+138=0 equation:

X^2+24X+138=0

a = 1; b = 24; c = +138;
Δ = b2-4ac
Δ = 242-4·1·138
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{6}}{2*1}=\frac{-24-2\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{6}}{2*1}=\frac{-24+2\sqrt{6}}{2}
$