24x^2-49-40=0

Solution for 24x^2-49-40=0 equation:

24x^2-49-40=0

We add all the numbers together, and all the variables

24x^2-89=0

a = 24; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·24·(-89)
Δ = 8544
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:

$\sqrt{\Delta}=\sqrt{8544}=\sqrt{16*534}=\sqrt{16}*\sqrt{534}=4\sqrt{534}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{534}}{2*24}=\frac{0-4\sqrt{534}}{48}
=-\frac{4\sqrt{534}}{48}
=-\frac{\sqrt{534}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{534}}{2*24}=\frac{0+4\sqrt{534}}{48}
=\frac{4\sqrt{534}}{48}
=\frac{\sqrt{534}}{12}
$