x(x+1)=800

Solution for x(x+1)=800 equation:

x(x+1)=800

We move all terms to the left:

x(x+1)-(800)=0

We multiply parentheses

x^2+x-800=0

a = 1; b = 1; c = -800;
Δ = b2-4ac
Δ = 12-4·1·(-800)
Δ = 3201
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{3201}}{2*1}=\frac{-1-\sqrt{3201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3201}}{2*1}=\frac{-1+\sqrt{3201}}{2}
$