X(x+1)=0.24

Solution for X(x+1)=0.24 equation:

X(X+1)=0.24

We move all terms to the left:

X(X+1)-(0.24)=0

We add all the numbers together, and all the variables

X(X+1)-0.24=0

We multiply parentheses

X^2+X-0.24=0

a = 1; b = 1; c = -0.24;
Δ = b2-4ac
Δ = 12-4·1·(-0.24)
Δ = 1.96
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{1.96}}{2*1}=\frac{-1-\sqrt{1.96}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1.96}}{2*1}=\frac{-1+\sqrt{1.96}}{2}
$