437=-0.5x^2+36x-137

Solution for 437=-0.5x^2+36x-137 equation:

437=-0.5x^2+36x-137

We move all terms to the left:

437-(-0.5x^2+36x-137)=0

We get rid of parentheses

0.5x^2-36x+137+437=0

We add all the numbers together, and all the variables

0.5x^2-36x+574=0

a = 0.5; b = -36; c = +574;
Δ = b2-4ac
Δ = -362-4·0.5·574
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{37}}{2*0.5}=\frac{36-2\sqrt{37}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{37}}{2*0.5}=\frac{36+2\sqrt{37}}{1}
$