356=-0.5x^2+36x-182

Solution for 356=-0.5x^2+36x-182 equation:

356=-0.5x^2+36x-182

We move all terms to the left:

356-(-0.5x^2+36x-182)=0

We get rid of parentheses

0.5x^2-36x+182+356=0

We add all the numbers together, and all the variables

0.5x^2-36x+538=0

a = 0.5; b = -36; c = +538;
Δ = b2-4ac
Δ = -362-4·0.5·538
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{55}}{2*0.5}=\frac{36-2\sqrt{55}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{55}}{2*0.5}=\frac{36+2\sqrt{55}}{1}
$