600=x*(x+1)*0.5

Solution for 600=x*(x+1)*0.5 equation:

600=x(x+1)*0.5

We move all terms to the left:

600-(x(x+1)*0.5)=0


We calculate terms in parentheses: -(x(x+1)*0.5), so:

x(x+1)*0.5

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+600=0

We add all the numbers together, and all the variables

-1x^2-1x+600=0

a = -1; b = -1; c = +600;
Δ = b2-4ac
Δ = -12-4·(-1)·600
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*-1}=\frac{50}{-2}
=-25
$