32X^2+40y^2-24=0

Solution for 32X^2+40y^2-24=0 equation:

32X^2+40X^2-24=0

We add all the numbers together, and all the variables

72X^2-24=0

a = 72; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·72·(-24)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*72}=\frac{0-48\sqrt{3}}{144}
=-\frac{48\sqrt{3}}{144}
=-\frac{\sqrt{3}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*72}=\frac{0+48\sqrt{3}}{144}
=\frac{48\sqrt{3}}{144}
=\frac{\sqrt{3}}{3}
$