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500-0.55556x(x-1200)=195
We move all terms to the left:
500-0.55556x(x-1200)-(195)=0
We add all the numbers together, and all the variables
-0.55556x(x-1200)+305=0
We multiply parentheses
-0x^2-0x+305=0
We add all the numbers together, and all the variables
-1x^2-1x+305=0
a = -1; b = -1; c = +305;
Δ = b2-4ac
Δ = -12-4·(-1)·305
Δ = 1221
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1221}}{2*-1}=\frac{1-\sqrt{1221}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1221}}{2*-1}=\frac{1+\sqrt{1221}}{-2} $
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