10.2d+1/6=6(1/3d+1)

Solution for 10.2d+1/6=6(1/3d+1) equation:

10.2d+1/6=6(1/3d+1)

We move all terms to the left:

10.2d+1/6-(6(1/3d+1))=0


Domain of the equation: 3d+1))!=0

d∈R


We calculate fractions


10.2d+()/3d+3d/3d=0

Fractions to decimals

()/3d+10.2d+1=0

We multiply all the terms by the denominator


(10.2d)*3d+1*3d+()=0

We add all the numbers together, and all the variables

(+10.2d)*3d+1*3d+()=0

We add all the numbers together, and all the variables

(+10.2d)*3d+1*3d=0

We multiply parentheses

30d^2+1*3d=0

Wy multiply elements

30d^2+3d=0

a = 30; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·30·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*30}=\frac{-6}{60}
=-1/10
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*30}=\frac{0}{60}
=0
$