0.5x^2+36x-176=418

Solution for 0.5x^2+36x-176=418 equation:

0.5x^2+36x-176=418

We move all terms to the left:

0.5x^2+36x-176-(418)=0

We add all the numbers together, and all the variables

0.5x^2+36x-594=0

a = 0.5; b = 36; c = -594;
Δ = b2-4ac
Δ = 362-4·0.5·(-594)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{69}}{2*0.5}=\frac{-36-6\sqrt{69}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{69}}{2*0.5}=\frac{-36+6\sqrt{69}}{1}
$