x^2+22x+46=0

Solution for x^2+22x+46=0 equation:

x^2+22x+46=0

a = 1; b = 22; c = +46;
Δ = b2-4ac
Δ = 222-4·1·46
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10\sqrt{3}}{2*1}=\frac{-22-10\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10\sqrt{3}}{2*1}=\frac{-22+10\sqrt{3}}{2}
$