-2/3r+3=1-2r

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

-2/3r+3=1-2r

We move all terms to the left:

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


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2/3r+2r-1+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

6r^2-3r+9r-2=0

We add all the numbers together, and all the variables

6r^2+6r-2=0

a = 6; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·6·(-2)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*6}=\frac{-6-2\sqrt{21}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*6}=\frac{-6+2\sqrt{21}}{12}
$