370=0.5x^2+36x-188

Solution for 370=0.5x^2+36x-188 equation:

370=0.5x^2+36x-188

We move all terms to the left:

370-(0.5x^2+36x-188)=0

We get rid of parentheses

-0.5x^2-36x+188+370=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 = 2412
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:

$\sqrt{\Delta}=\sqrt{2412}=\sqrt{36*67}=\sqrt{36}*\sqrt{67}=6\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{67}}{2*-0.5}=\frac{36-6\sqrt{67}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{67}}{2*-0.5}=\frac{36+6\sqrt{67}}{-1}
$