-0.5x^2+36x-169=353

Solution for -0.5x^2+36x-169=353 equation:

-0.5x^2+36x-169=353

We move all terms to the left:

-0.5x^2+36x-169-(353)=0

We add all the numbers together, and all the variables

-0.5x^2+36x-522=0

a = -0.5; b = 36; c = -522;
Δ = b2-4ac
Δ = 362-4·(-0.5)·(-522)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{7}}{2*-0.5}=\frac{-36-6\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{7}}{2*-0.5}=\frac{-36+6\sqrt{7}}{-1}
$