6r+12=2r^2+8r

Solution for 6r+12=2r^2+8r equation:

6r+12=2r^2+8r

We move all terms to the left:

6r+12-(2r^2+8r)=0

We get rid of parentheses

-2r^2+6r-8r+12=0

We add all the numbers together, and all the variables

-2r^2-2r+12=0

a = -2; b = -2; c = +12;
Δ = b2-4ac
Δ = -22-4·(-2)·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-2}=\frac{-8}{-4}
=+2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-2}=\frac{12}{-4}
=-3
$