X^2+46x+353=0

Solution for X^2+46x+353=0 equation:

X^2+46X+353=0

a = 1; b = 46; c = +353;
Δ = b2-4ac
Δ = 462-4·1·353
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-8\sqrt{11}}{2*1}=\frac{-46-8\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+8\sqrt{11}}{2*1}=\frac{-46+8\sqrt{11}}{2}
$