6d+8=14/3d

Solution for 6d+8=14/3d equation:

6d+8=14/3d

We move all terms to the left:

6d+8-(14/3d)=0


Domain of the equation: 3d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

6d-(+14/3d)+8=0

We get rid of parentheses

6d-14/3d+8=0

We multiply all the terms by the denominator


6d*3d+8*3d-14=0

Wy multiply elements

18d^2+24d-14=0

a = 18; b = 24; c = -14;
Δ = b2-4ac
Δ = 242-4·18·(-14)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{11}}{2*18}=\frac{-24-12\sqrt{11}}{36}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{11}}{2*18}=\frac{-24+12\sqrt{11}}{36}
$