24o(o+16)=52

Solution for 24o(o+16)=52 equation:

24o(o+16)=52

We move all terms to the left:

24o(o+16)-(52)=0

We multiply parentheses

24o^2+384o-52=0

a = 24; b = 384; c = -52;
Δ = b2-4ac
Δ = 3842-4·24·(-52)
Δ = 152448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$o_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$o_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152448}=\sqrt{64*2382}=\sqrt{64}*\sqrt{2382}=8\sqrt{2382}$
$o_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-8\sqrt{2382}}{2*24}=\frac{-384-8\sqrt{2382}}{48}
$
$o_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+8\sqrt{2382}}{2*24}=\frac{-384+8\sqrt{2382}}{48}
$