x(x+1)=0.65*0.65

Solution for x(x+1)=0.65*0.65 equation:

x(x+1)=0.65*0.65

We move all terms to the left:

x(x+1)-(0.65*0.65)=0

We add all the numbers together, and all the variables

x(x+1)-(0.4225)=0

We add all the numbers together, and all the variables

x(x+1)-0.4225=0

We multiply parentheses

x^2+x-0.4225=0

a = 1; b = 1; c = -0.4225;
Δ = b2-4ac
Δ = 12-4·1·(-0.4225)
Δ = 2.69
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{2.69}}{2*1}=\frac{-1-\sqrt{2.69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2.69}}{2*1}=\frac{-1+\sqrt{2.69}}{2}
$