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82.5x-(5.5x)(x/2)=0
We add all the numbers together, and all the variables
82.5x-(+5.5x)(+x/2)=0
We multiply parentheses ..
-(+5x^2)+82.5x=0
We get rid of parentheses
-5x^2+82.5x=0
a = -5; b = 82.5; c = 0;
Δ = b2-4ac
Δ = 82.52-4·(-5)·0
Δ = 6806.25
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{-(82.5)-\sqrt{6806.25}}{2*-5}=\frac{-82.5-\sqrt{6806.25}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82.5)+\sqrt{6806.25}}{2*-5}=\frac{-82.5+\sqrt{6806.25}}{-10} $
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