6r^2=12-r

Solution for 6r^2=12-r equation:

6r^2=12-r

We move all terms to the left:

6r^2-(12-r)=0

We add all the numbers together, and all the variables

6r^2-(-1r+12)=0

We get rid of parentheses

6r^2+1r-12=0

We add all the numbers together, and all the variables

6r^2+r-12=0

a = 6; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·6·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*6}=\frac{-18}{12}
=-1+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*6}=\frac{16}{12}
=1+1/3
$