-30=-10(d+90)d=

Solution for -30=-10(d+90)d= equation:

-30=-10(d+90)d=

We move all terms to the left:

-30-(-10(d+90)d)=0


We calculate terms in parentheses: -(-10(d+90)d), so:

-10(d+90)d

We multiply parentheses

-10d^2-900d

Back to the equation:

-(-10d^2-900d)


We get rid of parentheses

10d^2+900d-30=0

a = 10; b = 900; c = -30;
Δ = b2-4ac
Δ = 9002-4·10·(-30)
Δ = 811200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{811200}=\sqrt{270400*3}=\sqrt{270400}*\sqrt{3}=520\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-520\sqrt{3}}{2*10}=\frac{-900-520\sqrt{3}}{20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+520\sqrt{3}}{2*10}=\frac{-900+520\sqrt{3}}{20}
$