325-75=(x-200)x.25x

Solution for 325-75=(x-200)x.25x equation:

325-75=(x-200)x.25x

We move all terms to the left:

325-75-((x-200)x.25x)=0

We add all the numbers together, and all the variables

-((x-200)x.25x)+250=0


We calculate terms in parentheses: -((x-200)x.25x), so:

(x-200)x.25x

We multiply parentheses

x^2-200x

Back to the equation:

-(x^2-200x)


We get rid of parentheses

-x^2+200x+250=0

We add all the numbers together, and all the variables

-1x^2+200x+250=0

a = -1; b = 200; c = +250;
Δ = b2-4ac
Δ = 2002-4·(-1)·250
Δ = 41000
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:

$\sqrt{\Delta}=\sqrt{41000}=\sqrt{100*410}=\sqrt{100}*\sqrt{410}=10\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-10\sqrt{410}}{2*-1}=\frac{-200-10\sqrt{410}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+10\sqrt{410}}{2*-1}=\frac{-200+10\sqrt{410}}{-2}
$