0=(-7d+12)(-2d+8)

Solution for 0=(-7d+12)(-2d+8) equation:

0=(-7d+12)(-2d+8)

We move all terms to the left:

0-((-7d+12)(-2d+8))=0

We add all the numbers together, and all the variables

-((-7d+12)(-2d+8))=0

We multiply parentheses ..

-((+14d^2-56d-24d+96))=0


We calculate terms in parentheses: -((+14d^2-56d-24d+96)), so:

(+14d^2-56d-24d+96)

We get rid of parentheses

14d^2-56d-24d+96

We add all the numbers together, and all the variables

14d^2-80d+96

Back to the equation:

-(14d^2-80d+96)


We get rid of parentheses

-14d^2+80d-96=0

a = -14; b = 80; c = -96;
Δ = b2-4ac
Δ = 802-4·(-14)·(-96)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-32}{2*-14}=\frac{-112}{-28}
=+4
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+32}{2*-14}=\frac{-48}{-28}
=1+5/7
$