x^2+36x+105=0

Solution for x^2+36x+105=0 equation:

x^2+36x+105=0

a = 1; b = 36; c = +105;
Δ = b2-4ac
Δ = 362-4·1·105
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{219}}{2*1}=\frac{-36-2\sqrt{219}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{219}}{2*1}=\frac{-36+2\sqrt{219}}{2}
$