x^2+22x+103=0

Solution for x^2+22x+103=0 equation:

x^2+22x+103=0

a = 1; b = 22; c = +103;
Δ = b2-4ac
Δ = 222-4·1·103
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{2}}{2*1}=\frac{-22-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{2}}{2*1}=\frac{-22+6\sqrt{2}}{2}
$