24r^2-76r+32=0

Solution for 24r^2-76r+32=0 equation:

24r^2-76r+32=0

a = 24; b = -76; c = +32;
Δ = b2-4ac
Δ = -762-4·24·32
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{-(-76)-52}{2*24}=\frac{24}{48}
=1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+52}{2*24}=\frac{128}{48}
=2+2/3
$