2604=6r*3r+r

Solution for 2604=6r*3r+r equation:

2604=6r*3r+r

We move all terms to the left:

2604-(6r*3r+r)=0

We add all the numbers together, and all the variables

-(+r+6r*3r)+2604=0

We get rid of parentheses

-r-6r*3r+2604=0

We add all the numbers together, and all the variables

-1r-6r*3r+2604=0

Wy multiply elements

-18r^2-1r+2604=0

a = -18; b = -1; c = +2604;
Δ = b2-4ac
Δ = -12-4·(-18)·2604
Δ = 187489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{187489}=433$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-433}{2*-18}=\frac{-432}{-36}
=+12
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+433}{2*-18}=\frac{434}{-36}
=-12+1/18
$