(3d+1)(6d+8)=90

Solution for (3d+1)(6d+8)=90 equation:

(3d+1)(6d+8)=90

We move all terms to the left:

(3d+1)(6d+8)-(90)=0

We multiply parentheses ..

(+18d^2+24d+6d+8)-90=0

We get rid of parentheses

18d^2+24d+6d+8-90=0

We add all the numbers together, and all the variables

18d^2+30d-82=0

a = 18; b = 30; c = -82;
Δ = b2-4ac
Δ = 302-4·18·(-82)
Δ = 6804
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:

$\sqrt{\Delta}=\sqrt{6804}=\sqrt{324*21}=\sqrt{324}*\sqrt{21}=18\sqrt{21}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{21}}{2*18}=\frac{-30-18\sqrt{21}}{36}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{21}}{2*18}=\frac{-30+18\sqrt{21}}{36}
$