410=-0.5x^2+36x-148

Solution for 410=-0.5x^2+36x-148 equation:

410=-0.5x^2+36x-148

We move all terms to the left:

410-(-0.5x^2+36x-148)=0

We get rid of parentheses

0.5x^2-36x+148+410=0

We add all the numbers together, and all the variables

0.5x^2-36x+558=0

a = 0.5; b = -36; c = +558;
Δ = b2-4ac
Δ = -362-4·0.5·558
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{5}}{2*0.5}=\frac{36-6\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{5}}{2*0.5}=\frac{36+6\sqrt{5}}{1}
$