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0=0.5x^2+36x-594
We move all terms to the left:
0-(0.5x^2+36x-594)=0
We add all the numbers together, and all the variables
-(0.5x^2+36x-594)=0
We get rid of parentheses
-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} $
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