X(x+1)=22.5

Solution for X(x+1)=22.5 equation:

X(X+1)=22.5

We move all terms to the left:

X(X+1)-(22.5)=0

We add all the numbers together, and all the variables

X(X+1)-22.5=0

We multiply parentheses

X^2+X-22.5=0

a = 1; b = 1; c = -22.5;
Δ = b2-4ac
Δ = 12-4·1·(-22.5)
Δ = 91
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{91}}{2*1}=\frac{-1-\sqrt{91}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{91}}{2*1}=\frac{-1+\sqrt{91}}{2}
$