24r2=-8r+112

Solution for 24r2=-8r+112 equation:

24r^2=-8r+112

We move all terms to the left:

24r^2-(-8r+112)=0

We get rid of parentheses

24r^2+8r-112=0

a = 24; b = 8; c = -112;
Δ = b2-4ac
Δ = 82-4·24·(-112)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-104}{2*24}=\frac{-112}{48}
=-2+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+104}{2*24}=\frac{96}{48}
=2
$