9(d+7)d=2

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

9(d+7)d=2

We move all terms to the left:

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

We multiply parentheses

9d^2+63d-2=0

a = 9; b = 63; c = -2;
Δ = b2-4ac
Δ = 632-4·9·(-2)
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{449}}{2*9}=\frac{-63-3\sqrt{449}}{18}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{449}}{2*9}=\frac{-63+3\sqrt{449}}{18}
$