102/3d+1=16-d

Solution for 102/3d+1=16-d equation:

102/3d+1=16-d

We move all terms to the left:

102/3d+1-(16-d)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We add all the numbers together, and all the variables

102/3d-(-1d+16)+1=0

We get rid of parentheses

102/3d+1d-16+1=0

We multiply all the terms by the denominator


1d*3d-16*3d+1*3d+102=0

Wy multiply elements

3d^2-48d+3d+102=0

We add all the numbers together, and all the variables

3d^2-45d+102=0

a = 3; b = -45; c = +102;
Δ = b2-4ac
Δ = -452-4·3·102
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{89}}{2*3}=\frac{45-3\sqrt{89}}{6}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{89}}{2*3}=\frac{45+3\sqrt{89}}{6}
$