x(x+200)=205

Solution for x(x+200)=205 equation:

x(x+200)=205

We move all terms to the left:

x(x+200)-(205)=0

We multiply parentheses

x^2+200x-205=0

a = 1; b = 200; c = -205;
Δ = b2-4ac
Δ = 2002-4·1·(-205)
Δ = 40820
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:

$\sqrt{\Delta}=\sqrt{40820}=\sqrt{4*10205}=\sqrt{4}*\sqrt{10205}=2\sqrt{10205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10205}}{2*1}=\frac{-200-2\sqrt{10205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10205}}{2*1}=\frac{-200+2\sqrt{10205}}{2}
$