2+7d(d+1)=9+7d

Solution for 2+7d(d+1)=9+7d equation:

2+7d(d+1)=9+7d

We move all terms to the left:

2+7d(d+1)-(9+7d)=0

We add all the numbers together, and all the variables

7d(d+1)-(7d+9)+2=0

We multiply parentheses

7d^2+7d-(7d+9)+2=0

We get rid of parentheses

7d^2+7d-7d-9+2=0

We add all the numbers together, and all the variables

7d^2-7=0

a = 7; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·7·(-7)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*7}=\frac{-14}{14}
=-1
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*7}=\frac{14}{14}
=1
$