1+x(x+1)=156

Solution for 1+x(x+1)=156 equation:

1+x(x+1)=156

We move all terms to the left:

1+x(x+1)-(156)=0

We add all the numbers together, and all the variables

x(x+1)-155=0

We multiply parentheses

x^2+x-155=0

a = 1; b = 1; c = -155;
Δ = b2-4ac
Δ = 12-4·1·(-155)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{69}}{2*1}=\frac{-1-3\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{69}}{2*1}=\frac{-1+3\sqrt{69}}{2}
$