2/3r-7=r

Solution for 2/3r-7=r equation:

2/3r-7=r

We move all terms to the left:

2/3r-7-(r)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

-1r+2/3r-7=0

We multiply all the terms by the denominator


-1r*3r-7*3r+2=0

Wy multiply elements

-3r^2-21r+2=0

a = -3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-3)·2
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{465}}{2*-3}=\frac{21-\sqrt{465}}{-6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*-3}=\frac{21+\sqrt{465}}{-6}
$