(13+r)5rr=12

Solution for (13+r)5rr=12 equation:

(13+r)5rr=12

We move all terms to the left:

(13+r)5rr-(12)=0

We add all the numbers together, and all the variables

(r+13)5rr-12=0

We multiply parentheses

5r^2+65r-12=0

a = 5; b = 65; c = -12;
Δ = b2-4ac
Δ = 652-4·5·(-12)
Δ = 4465
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{-(65)-\sqrt{4465}}{2*5}=\frac{-65-\sqrt{4465}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4465}}{2*5}=\frac{-65+\sqrt{4465}}{10}
$