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10.000=x(-20x+1200)
We move all terms to the left:
10.000-(x(-20x+1200))=0
We add all the numbers together, and all the variables
-(x(-20x+1200))+10=0
We calculate terms in parentheses: -(x(-20x+1200)), so:We get rid of parentheses
x(-20x+1200)
We multiply parentheses
-20x^2+1200x
Back to the equation:
-(-20x^2+1200x)
20x^2-1200x+10=0
a = 20; b = -1200; c = +10;
Δ = b2-4ac
Δ = -12002-4·20·10
Δ = 1439200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1439200}=\sqrt{400*3598}=\sqrt{400}*\sqrt{3598}=20\sqrt{3598}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-20\sqrt{3598}}{2*20}=\frac{1200-20\sqrt{3598}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+20\sqrt{3598}}{2*20}=\frac{1200+20\sqrt{3598}}{40} $
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