2r+2/3r-5=1

Solution for 2r+2/3r-5=1 equation:

2r+2/3r-5=1

We move all terms to the left:

2r+2/3r-5-(1)=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+2/3r-6=0

We multiply all the terms by the denominator


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

Wy multiply elements

6r^2-18r+2=0

a = 6; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·6·2
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{69}}{2*6}=\frac{18-2\sqrt{69}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{69}}{2*6}=\frac{18+2\sqrt{69}}{12}
$