2/9*r=6

Solution for 2/9*r=6 equation:

2/9*r=6

We move all terms to the left:

2/9*r-(6)=0


Domain of the equation: 9*r!=0

r!=0/1

r!=0

r∈R


We multiply all the terms by the denominator


-6*9*r+2=0

Wy multiply elements

-54r*r+2=0

Wy multiply elements

-54r^2+2=0

a = -54; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-54)·2
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-54}=\frac{0-12\sqrt{3}}{-108}
=-\frac{12\sqrt{3}}{-108}
=-\frac{\sqrt{3}}{-9}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-54}=\frac{0+12\sqrt{3}}{-108}
=\frac{12\sqrt{3}}{-108}
=\frac{\sqrt{3}}{-9}
$