8d-(1/3)(6-9d)=42

Solution for 8d-(1/3)(6-9d)=42 equation:

8d-(1/3)(6-9d)=42

We move all terms to the left:

8d-(1/3)(6-9d)-(42)=0


Domain of the equation: 3)(6-9d)!=0

d∈R


We add all the numbers together, and all the variables

8d-(+1/3)(-9d+6)-42=0

We multiply parentheses ..

-(-9d^2+1/3*6)+8d-42=0

We multiply all the terms by the denominator


-(-9d^2+1+8d*3*6)-42*3*6)=0

We add all the numbers together, and all the variables

-(-9d^2+1+8d*3*6)=0

We get rid of parentheses

9d^2-8d*3*6-1=0

Wy multiply elements

9d^2-144d*6-1=0

Wy multiply elements

9d^2-864d-1=0

a = 9; b = -864; c = -1;
Δ = b2-4ac
Δ = -8642-4·9·(-1)
Δ = 746532
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:

$\sqrt{\Delta}=\sqrt{746532}=\sqrt{36*20737}=\sqrt{36}*\sqrt{20737}=6\sqrt{20737}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-864)-6\sqrt{20737}}{2*9}=\frac{864-6\sqrt{20737}}{18}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-864)+6\sqrt{20737}}{2*9}=\frac{864+6\sqrt{20737}}{18}
$