100=25d(1+d/3)

Solution for 100=25d(1+d/3) equation:

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:

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)


We get rid of parentheses

-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
$