25=(x-100)x

Solution for 25=(x-100)x equation:

25=(x-100)x

We move all terms to the left:

25-((x-100)x)=0


We calculate terms in parentheses: -((x-100)x), so:

(x-100)x

We multiply parentheses

x^2-100x

Back to the equation:

-(x^2-100x)


We get rid of parentheses

-x^2+100x+25=0

We add all the numbers together, and all the variables

-1x^2+100x+25=0

a = -1; b = 100; c = +25;
Δ = b2-4ac
Δ = 1002-4·(-1)·25
Δ = 10100
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:

$\sqrt{\Delta}=\sqrt{10100}=\sqrt{100*101}=\sqrt{100}*\sqrt{101}=10\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{101}}{2*-1}=\frac{-100-10\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{101}}{2*-1}=\frac{-100+10\sqrt{101}}{-2}
$