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100=25d(1+d/3)
We move all terms to the left:
100-(25d(1+d/3))=0
We add all the numbers together, and all the variables
-(25d(d/3+1))+100=0
We multiply all the terms by the denominator
-(25d(d+100*3+1))=0
We calculate terms in parentheses: -(25d(d+100*3+1)), so:We get rid of parentheses
25d(d+100*3+1)
We add all the numbers together, and all the variables
25d(d+301)
We multiply parentheses
25d^2+7525d
Back to the equation:
-(25d^2+7525d)
-25d^2-7525d=0
a = -25; b = -7525; c = 0;
Δ = b2-4ac
Δ = -75252-4·(-25)·0
Δ = 56625625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{56625625}=7525$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7525)-7525}{2*-25}=\frac{0}{-50} =0 $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7525)+7525}{2*-25}=\frac{15050}{-50} =-301 $
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