X(x+5)=414

Solution for X(x+5)=414 equation:

X(X+5)=414

We move all terms to the left:

X(X+5)-(414)=0

We multiply parentheses

X^2+5X-414=0

a = 1; b = 5; c = -414;
Δ = b2-4ac
Δ = 52-4·1·(-414)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-41}{2*1}=\frac{-46}{2}
=-23
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+41}{2*1}=\frac{36}{2}
=18
$