489=-0.5x^2+36x-123

Solution for 489=-0.5x^2+36x-123 equation:

489=-0.5x^2+36x-123

We move all terms to the left:

489-(-0.5x^2+36x-123)=0

We get rid of parentheses

0.5x^2-36x+123+489=0

We add all the numbers together, and all the variables

0.5x^2-36x+612=0

a = 0.5; b = -36; c = +612;
Δ = b2-4ac
Δ = -362-4·0.5·612
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{2}}{2*0.5}=\frac{36-6\sqrt{2}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{2}}{2*0.5}=\frac{36+6\sqrt{2}}{1}
$