1/3d-6=3d-30

Solution for 1/3d-6=3d-30 equation:

1/3d-6=3d-30

We move all terms to the left:

1/3d-6-(3d-30)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We get rid of parentheses

1/3d-3d+30-6=0

We multiply all the terms by the denominator


-3d*3d+30*3d-6*3d+1=0

Wy multiply elements

-9d^2+90d-18d+1=0

We add all the numbers together, and all the variables

-9d^2+72d+1=0

a = -9; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-9)·1
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{145}}{2*-9}=\frac{-72-6\sqrt{145}}{-18}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{145}}{2*-9}=\frac{-72+6\sqrt{145}}{-18}
$