25,000=-0.5x^2-200x

Solution for 25,000=-0.5x^2-200x equation:

25.000=-0.5x^2-200x

We move all terms to the left:

25.000-(-0.5x^2-200x)=0

We add all the numbers together, and all the variables

-(-0.5x^2-200x)+25=0

We get rid of parentheses

0.5x^2+200x+25=0

a = 0.5; b = 200; c = +25;
Δ = b2-4ac
Δ = 2002-4·0.5·25
Δ = 39950
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:

$\sqrt{\Delta}=\sqrt{39950}=\sqrt{25*1598}=\sqrt{25}*\sqrt{1598}=5\sqrt{1598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-5\sqrt{1598}}{2*0.5}=\frac{-200-5\sqrt{1598}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+5\sqrt{1598}}{2*0.5}=\frac{-200+5\sqrt{1598}}{1}
$