x*(x-3)/2=1200

Solution for x*(x-3)/2=1200 equation:

x(x-3)/2=1200

We move all terms to the left:

x(x-3)/2-(1200)=0

We multiply all the terms by the denominator


x(x-3)-1200*2=0

We add all the numbers together, and all the variables

x(x-3)-2400=0

We multiply parentheses

x^2-3x-2400=0

a = 1; b = -3; c = -2400;
Δ = b2-4ac
Δ = -32-4·1·(-2400)
Δ = 9609
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{-(-3)-\sqrt{9609}}{2*1}=\frac{3-\sqrt{9609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{9609}}{2*1}=\frac{3+\sqrt{9609}}{2}
$