-11r^2+6=-12r^2-7r

Solution for -11r^2+6=-12r^2-7r equation:

-11r^2+6=-12r^2-7r

We move all terms to the left:

-11r^2+6-(-12r^2-7r)=0

We get rid of parentheses

-11r^2+12r^2+7r+6=0

We add all the numbers together, and all the variables

r^2+7r+6=0

a = 1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*1}=\frac{-12}{2}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*1}=\frac{-2}{2}
=-1
$