3d(5d+8)=34-8

Solution for 3d(5d+8)=34-8 equation:

3d(5d+8)=34-8

We move all terms to the left:

3d(5d+8)-(34-8)=0

We add all the numbers together, and all the variables

3d(5d+8)-26=0

We multiply parentheses

15d^2+24d-26=0

a = 15; b = 24; c = -26;
Δ = b2-4ac
Δ = 242-4·15·(-26)
Δ = 2136
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:

$\sqrt{\Delta}=\sqrt{2136}=\sqrt{4*534}=\sqrt{4}*\sqrt{534}=2\sqrt{534}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{534}}{2*15}=\frac{-24-2\sqrt{534}}{30}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{534}}{2*15}=\frac{-24+2\sqrt{534}}{30}
$