X(x+1)=37

Solution for X(x+1)=37 equation:

X(X+1)=37

We move all terms to the left:

X(X+1)-(37)=0

We multiply parentheses

X^2+X-37=0

a = 1; b = 1; c = -37;
Δ = b2-4ac
Δ = 12-4·1·(-37)
Δ = 149
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{-(1)-\sqrt{149}}{2*1}=\frac{-1-\sqrt{149}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{149}}{2*1}=\frac{-1+\sqrt{149}}{2}
$