24r^2+32-76=0

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

24r^2+32-76=0

We add all the numbers together, and all the variables

24r^2-44=0

a = 24; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·24·(-44)
Δ = 4224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*24}=\frac{0-8\sqrt{66}}{48}
=-\frac{8\sqrt{66}}{48}
=-\frac{\sqrt{66}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*24}=\frac{0+8\sqrt{66}}{48}
=\frac{8\sqrt{66}}{48}
=\frac{\sqrt{66}}{6}
$