X(x+1)=510

Solution for X(x+1)=510 equation:

X(X+1)=510

We move all terms to the left:

X(X+1)-(510)=0

We multiply parentheses

X^2+X-510=0

a = 1; b = 1; c = -510;
Δ = b2-4ac
Δ = 12-4·1·(-510)
Δ = 2041
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{2041}}{2*1}=\frac{-1-\sqrt{2041}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2041}}{2*1}=\frac{-1+\sqrt{2041}}{2}
$