6r^2-12r=48

Solution for 6r^2-12r=48 equation:

6r^2-12r=48

We move all terms to the left:

6r^2-12r-(48)=0

a = 6; b = -12; c = -48;
Δ = b2-4ac
Δ = -122-4·6·(-48)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*6}=\frac{-24}{12}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*6}=\frac{48}{12}
=4
$