X(x+1)+x=62

Solution for X(x+1)+x=62 equation:

X(X+1)+X=62

We move all terms to the left:

X(X+1)+X-(62)=0

We add all the numbers together, and all the variables

X+X(X+1)-62=0

We multiply parentheses

X^2+X+X-62=0

We add all the numbers together, and all the variables

X^2+2X-62=0

a = 1; b = 2; c = -62;
Δ = b2-4ac
Δ = 22-4·1·(-62)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{7}}{2*1}=\frac{-2-6\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{7}}{2*1}=\frac{-2+6\sqrt{7}}{2}
$