X(x+3)+1=625

Solution for X(x+3)+1=625 equation:

X(X+3)+1=625

We move all terms to the left:

X(X+3)+1-(625)=0

We add all the numbers together, and all the variables

X(X+3)-624=0

We multiply parentheses

X^2+3X-624=0

a = 1; b = 3; c = -624;
Δ = b2-4ac
Δ = 32-4·1·(-624)
Δ = 2505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{2505}}{2*1}=\frac{-3-\sqrt{2505}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{2505}}{2*1}=\frac{-3+\sqrt{2505}}{2}
$