d+4/3d=336

Solution for d+4/3d=336 equation:

d+4/3d=336

We move all terms to the left:

d+4/3d-(336)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We multiply all the terms by the denominator


d*3d-336*3d+4=0

Wy multiply elements

3d^2-1008d+4=0

a = 3; b = -1008; c = +4;
Δ = b2-4ac
Δ = -10082-4·3·4
Δ = 1016016
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:

$\sqrt{\Delta}=\sqrt{1016016}=\sqrt{16*63501}=\sqrt{16}*\sqrt{63501}=4\sqrt{63501}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63501}}{2*3}=\frac{1008-4\sqrt{63501}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63501}}{2*3}=\frac{1008+4\sqrt{63501}}{6}
$