d^2=2(12-d)

Solution for d^2=2(12-d) equation:

d^2=2(12-d)

We move all terms to the left:

d^2-(2(12-d))=0

We add all the numbers together, and all the variables

d^2-(2(-1d+12))=0


We calculate terms in parentheses: -(2(-1d+12)), so:

2(-1d+12)

We multiply parentheses

-2d+24

Back to the equation:

-(-2d+24)


We get rid of parentheses

d^2+2d-24=0

a = 1; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*1}=\frac{-12}{2}
=-6
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*1}=\frac{8}{2}
=4
$