X(x-+1)=650

Solution for X(x-+1)=650 equation:

X(X-+1)=650

We move all terms to the left:

X(X-+1)-(650)=0

We add all the numbers together, and all the variables

X(+X)-650=0

We multiply parentheses

X^2-650=0

a = 1; b = 0; c = -650;
Δ = b2-4ac
Δ = 02-4·1·(-650)
Δ = 2600
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:

$\sqrt{\Delta}=\sqrt{2600}=\sqrt{100*26}=\sqrt{100}*\sqrt{26}=10\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{26}}{2*1}=\frac{0-10\sqrt{26}}{2}
=-\frac{10\sqrt{26}}{2}
=-5\sqrt{26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{26}}{2*1}=\frac{0+10\sqrt{26}}{2}
=\frac{10\sqrt{26}}{2}
=5\sqrt{26}
$