24x^2-32=196

Solution for 24x^2-32=196 equation:

24x^2-32=196

We move all terms to the left:

24x^2-32-(196)=0

We add all the numbers together, and all the variables

24x^2-228=0

a = 24; b = 0; c = -228;
Δ = b2-4ac
Δ = 02-4·24·(-228)
Δ = 21888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21888}=\sqrt{576*38}=\sqrt{576}*\sqrt{38}=24\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{38}}{2*24}=\frac{0-24\sqrt{38}}{48}
=-\frac{24\sqrt{38}}{48}
=-\frac{\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{38}}{2*24}=\frac{0+24\sqrt{38}}{48}
=\frac{24\sqrt{38}}{48}
=\frac{\sqrt{38}}{2}
$