999=(x/2)(1+x)

Solution for 999=(x/2)(1+x) equation:

999=(x/2)(1+x)

We move all terms to the left:

999-((x/2)(1+x))=0


Domain of the equation: 2)(1+x))!=0

x∈R


We add all the numbers together, and all the variables

-((+x/2)(x+1))+999=0

We multiply parentheses ..

-((+x^2+x))+999=0


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

(+x^2+x)

We get rid of parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+999=0

We add all the numbers together, and all the variables

-1x^2-1x+999=0

a = -1; b = -1; c = +999;
Δ = b2-4ac
Δ = -12-4·(-1)·999
Δ = 3997
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{-(-1)-\sqrt{3997}}{2*-1}=\frac{1-\sqrt{3997}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3997}}{2*-1}=\frac{1+\sqrt{3997}}{-2}
$