2r+3/3r-6=6

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

2r+3/3r-6=6

We move all terms to the left:

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


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

2r+3/3r-12=0

We multiply all the terms by the denominator


2r*3r-12*3r+3=0

Wy multiply elements

6r^2-36r+3=0

a = 6; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·6·3
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{34}}{2*6}=\frac{36-6\sqrt{34}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{34}}{2*6}=\frac{36+6\sqrt{34}}{12}
$