362=-0.5x^2+36x-150

Solution for 362=-0.5x^2+36x-150 equation:

362=-0.5x^2+36x-150

We move all terms to the left:

362-(-0.5x^2+36x-150)=0

We get rid of parentheses

0.5x^2-36x+150+362=0

We add all the numbers together, and all the variables

0.5x^2-36x+512=0

a = 0.5; b = -36; c = +512;
Δ = b2-4ac
Δ = -362-4·0.5·512
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{17}}{2*0.5}=\frac{36-4\sqrt{17}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{17}}{2*0.5}=\frac{36+4\sqrt{17}}{1}
$