7500=x(-200-x)

Solution for 7500=x(-200-x) equation:

7500=x(-200-x)

We move all terms to the left:

7500-(x(-200-x))=0

We add all the numbers together, and all the variables

-(x(-1x-200))+7500=0


We calculate terms in parentheses: -(x(-1x-200)), so:

x(-1x-200)

We multiply parentheses

-1x^2-200x

Back to the equation:

-(-1x^2-200x)


We get rid of parentheses

1x^2+200x+7500=0

We add all the numbers together, and all the variables

x^2+200x+7500=0

a = 1; b = 200; c = +7500;
Δ = b2-4ac
Δ = 2002-4·1·7500
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-100}{2*1}=\frac{-300}{2}
=-150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+100}{2*1}=\frac{-100}{2}
=-50
$