0=x(12-0.025x)

Solution for 0=x(12-0.025x) equation:

0=x(12-0.025x)

We move all terms to the left:

0-(x(12-0.025x))=0

We add all the numbers together, and all the variables

-(x(-0.025x+12))+0=0

We add all the numbers together, and all the variables

-(x(-0.025x+12))=0


We calculate terms in parentheses: -(x(-0.025x+12)), so:

x(-0.025x+12)

We multiply parentheses

0x^2+12x

We add all the numbers together, and all the variables

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x=0

We add all the numbers together, and all the variables

-1x^2-12x=0

a = -1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-1)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-1}=\frac{24}{-2}
=-12
$