X(x+1)=1406

Solution for X(x+1)=1406 equation:

X(X+1)=1406

We move all terms to the left:

X(X+1)-(1406)=0

We multiply parentheses

X^2+X-1406=0

a = 1; b = 1; c = -1406;
Δ = b2-4ac
Δ = 12-4·1·(-1406)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-75}{2*1}=\frac{-76}{2}
=-38
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+75}{2*1}=\frac{74}{2}
=37
$