25=x(100-2x)

Solution for 25=x(100-2x) equation:

25=x(100-2x)

We move all terms to the left:

25-(x(100-2x))=0

We add all the numbers together, and all the variables

-(x(-2x+100))+25=0


We calculate terms in parentheses: -(x(-2x+100)), so:

x(-2x+100)

We multiply parentheses

-2x^2+100x

Back to the equation:

-(-2x^2+100x)


We get rid of parentheses

2x^2-100x+25=0

a = 2; b = -100; c = +25;
Δ = b2-4ac
Δ = -1002-4·2·25
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-70\sqrt{2}}{2*2}=\frac{100-70\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+70\sqrt{2}}{2*2}=\frac{100+70\sqrt{2}}{4}
$