x(x+1800)=41800

Solution for x(x+1800)=41800 equation:

x(x+1800)=41800

We move all terms to the left:

x(x+1800)-(41800)=0

We multiply parentheses

x^2+1800x-41800=0

a = 1; b = 1800; c = -41800;
Δ = b2-4ac
Δ = 18002-4·1·(-41800)
Δ = 3407200
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:

$\sqrt{\Delta}=\sqrt{3407200}=\sqrt{400*8518}=\sqrt{400}*\sqrt{8518}=20\sqrt{8518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-20\sqrt{8518}}{2*1}=\frac{-1800-20\sqrt{8518}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+20\sqrt{8518}}{2*1}=\frac{-1800+20\sqrt{8518}}{2}
$