10,000(x)=x(-20x+1200)

Solution for 10,000(x)=x(-20x+1200) equation:

10.000(x)=x(-20x+1200)

We move all terms to the left:

10.000(x)-(x(-20x+1200))=0


We calculate terms in parentheses: -(x(-20x+1200)), so:

x(-20x+1200)

We multiply parentheses

-20x^2+1200x

Back to the equation:

-(-20x^2+1200x)


We get rid of parentheses

20x^2-1200x+10.000x=0

We add all the numbers together, and all the variables

20x^2-1190x=0

a = 20; b = -1190; c = 0;
Δ = b2-4ac
Δ = -11902-4·20·0
Δ = 1416100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1416100}=1190$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1190)-1190}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1190)+1190}{2*20}=\frac{2380}{40}
=59+1/2
$