0.5x^2+0.5x=1800

Solution for 0.5x^2+0.5x=1800 equation:

0.5x^2+0.5x=1800

We move all terms to the left:

0.5x^2+0.5x-(1800)=0

a = 0.5; b = 0.5; c = -1800;
Δ = b2-4ac
Δ = 0.52-4·0.5·(-1800)
Δ = 3600.25
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{-(0.5)-\sqrt{3600.25}}{2*0.5}=\frac{-0.5-\sqrt{3600.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{3600.25}}{2*0.5}=\frac{-0.5+\sqrt{3600.25}}{1}
$