0=1000-2x-1.5*(x*x)

Solution for 0=1000-2x-1.5*(x*x) equation:

0=1000-2x-1.5(x*x)

We move all terms to the left:

0-(1000-2x-1.5(x*x))=0

We add all the numbers together, and all the variables

-(1000-2x-1.5(+x*x))+0=0

We add all the numbers together, and all the variables

-(1000-2x-1.5(+x*x))=0


We calculate terms in parentheses: -(1000-2x-1.5(+x*x)), so:

1000-2x-1.5(+x*x)

determiningTheFunctionDomain
-2x-1.5(+x*x)+1000

We multiply parentheses

-1.5x^2-2x+1000

Back to the equation:

-(-1.5x^2-2x+1000)


We get rid of parentheses

1.5x^2+2x-1000=0

a = 1.5; b = 2; c = -1000;
Δ = b2-4ac
Δ = 22-4·1.5·(-1000)
Δ = 6004
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:

$\sqrt{\Delta}=\sqrt{6004}=\sqrt{4*1501}=\sqrt{4}*\sqrt{1501}=2\sqrt{1501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1501}}{2*1.5}=\frac{-2-2\sqrt{1501}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1501}}{2*1.5}=\frac{-2+2\sqrt{1501}}{3}
$