200x+200x(x+1/2)=1250

Solution for 200x+200x(x+1/2)=1250 equation:

200x+200x(x+1/2)=1250

We move all terms to the left:

200x+200x(x+1/2)-(1250)=0

We add all the numbers together, and all the variables

200x+200x(+x+1/2)-1250=0

We multiply parentheses

200x^2+200x^2+200x-1250=0

We add all the numbers together, and all the variables

400x^2+200x-1250=0

a = 400; b = 200; c = -1250;
Δ = b2-4ac
Δ = 2002-4·400·(-1250)
Δ = 2040000
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:

$\sqrt{\Delta}=\sqrt{2040000}=\sqrt{40000*51}=\sqrt{40000}*\sqrt{51}=200\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200\sqrt{51}}{2*400}=\frac{-200-200\sqrt{51}}{800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200\sqrt{51}}{2*400}=\frac{-200+200\sqrt{51}}{800}
$