2/6r=3r-1

Solution for 2/6r=3r-1 equation:

2/6r=3r-1

We move all terms to the left:

2/6r-(3r-1)=0


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We get rid of parentheses

2/6r-3r+1=0

We multiply all the terms by the denominator


-3r*6r+1*6r+2=0

Wy multiply elements

-18r^2+6r+2=0

a = -18; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-18)·2
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*-18}=\frac{-6-6\sqrt{5}}{-36}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*-18}=\frac{-6+6\sqrt{5}}{-36}
$