X^2+40x+345=0

Solution for X^2+40x+345=0 equation:

X^2+40X+345=0

a = 1; b = 40; c = +345;
Δ = b2-4ac
Δ = 402-4·1·345
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{55}}{2*1}=\frac{-40-2\sqrt{55}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{55}}{2*1}=\frac{-40+2\sqrt{55}}{2}
$