X(x+1)=8.2

Solution for X(x+1)=8.2 equation:

X(X+1)=8.2

We move all terms to the left:

X(X+1)-(8.2)=0

We add all the numbers together, and all the variables

X(X+1)-8.2=0

We multiply parentheses

X^2+X-8.2=0

a = 1; b = 1; c = -8.2;
Δ = b2-4ac
Δ = 12-4·1·(-8.2)
Δ = 33.8
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{33.8}}{2*1}=\frac{-1-\sqrt{33.8}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33.8}}{2*1}=\frac{-1+\sqrt{33.8}}{2}
$