2r^2-12r=-16

Solution for 2r^2-12r=-16 equation:

2r^2-12r=-16

We move all terms to the left:

2r^2-12r-(-16)=0

We add all the numbers together, and all the variables

2r^2-12r+16=0

a = 2; b = -12; c = +16;
Δ = b2-4ac
Δ = -122-4·2·16
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*2}=\frac{8}{4}
=2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*2}=\frac{16}{4}
=4
$