100-2.5x=100+2.5x(5-x)

Solution for 100-2.5x=100+2.5x(5-x) equation:

100-2.5x=100+2.5x(5-x)

We move all terms to the left:

100-2.5x-(100+2.5x(5-x))=0

We add all the numbers together, and all the variables

-2.5x-(100+2.5x(-1x+5))+100=0


We calculate terms in parentheses: -(100+2.5x(-1x+5)), so:

100+2.5x(-1x+5)

determiningTheFunctionDomain
2.5x(-1x+5)+100

We multiply parentheses

-2x^2+10x+100

Back to the equation:

-(-2x^2+10x+100)


We get rid of parentheses

2x^2-10x-2.5x-100+100=0

We add all the numbers together, and all the variables

2x^2-12.5x=0

a = 2; b = -12.5; c = 0;
Δ = b2-4ac
Δ = -12.52-4·2·0
Δ = 156.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.5)-\sqrt{156.25}}{2*2}=\frac{12.5-\sqrt{156.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.5)+\sqrt{156.25}}{2*2}=\frac{12.5+\sqrt{156.25}}{4}
$