12r^2+12r+12=-13r

Solution for 12r^2+12r+12=-13r equation:

12r^2+12r+12=-13r

We move all terms to the left:

12r^2+12r+12-(-13r)=0

We get rid of parentheses

12r^2+12r+13r+12=0

We add all the numbers together, and all the variables

12r^2+25r+12=0

a = 12; b = 25; c = +12;
Δ = b2-4ac
Δ = 252-4·12·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7}{2*12}=\frac{-32}{24}
=-1+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7}{2*12}=\frac{-18}{24}
=-3/4
$