6r^2-32=-44r

Solution for 6r^2-32=-44r equation:

6r^2-32=-44r

We move all terms to the left:

6r^2-32-(-44r)=0

We get rid of parentheses

6r^2+44r-32=0

a = 6; b = 44; c = -32;
Δ = b2-4ac
Δ = 442-4·6·(-32)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-52}{2*6}=\frac{-96}{12}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+52}{2*6}=\frac{8}{12}
=2/3
$