0.1d=0.25d(d-30)

Solution for 0.1d=0.25d(d-30) equation:

0.1d=0.25d(d-30)

We move all terms to the left:

0.1d-(0.25d(d-30))=0


We calculate terms in parentheses: -(0.25d(d-30)), so:

0.25d(d-30)

We multiply parentheses

0d^2+0d

We add all the numbers together, and all the variables

d^2+d

Back to the equation:

-(d^2+d)


We get rid of parentheses

-d^2+0.1d-d=0

We add all the numbers together, and all the variables

-1d^2-0.9d=0

a = -1; b = -0.9; c = 0;
Δ = b2-4ac
Δ = -0.92-4·(-1)·0
Δ = 0.81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.9)-\sqrt{0.81}}{2*-1}=\frac{0.9-\sqrt{0.81}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{0.81}}{2*-1}=\frac{0.9+\sqrt{0.81}}{-2}
$