40x^2-192=0

Solution for 40x^2-192=0 equation:

40x^2-192=0

a = 40; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·40·(-192)
Δ = 30720
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:

$\sqrt{\Delta}=\sqrt{30720}=\sqrt{1024*30}=\sqrt{1024}*\sqrt{30}=32\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{30}}{2*40}=\frac{0-32\sqrt{30}}{80}
=-\frac{32\sqrt{30}}{80}
=-\frac{2\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{30}}{2*40}=\frac{0+32\sqrt{30}}{80}
=\frac{32\sqrt{30}}{80}
=\frac{2\sqrt{30}}{5}
$