4/3d+6d=22

Solution for 4/3d+6d=22 equation:

4/3d+6d=22

We move all terms to the left:

4/3d+6d-(22)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We add all the numbers together, and all the variables

6d+4/3d-22=0

We multiply all the terms by the denominator


6d*3d-22*3d+4=0

Wy multiply elements

18d^2-66d+4=0

a = 18; b = -66; c = +4;
Δ = b2-4ac
Δ = -662-4·18·4
Δ = 4068
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:

$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{113}}{2*18}=\frac{66-6\sqrt{113}}{36}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{113}}{2*18}=\frac{66+6\sqrt{113}}{36}
$