72x^2-9=0

Solution for 72x^2-9=0 equation:

72x^2-9=0

a = 72; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·72·(-9)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*72}=\frac{0-36\sqrt{2}}{144}
=-\frac{36\sqrt{2}}{144}
=-\frac{\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*72}=\frac{0+36\sqrt{2}}{144}
=\frac{36\sqrt{2}}{144}
=\frac{\sqrt{2}}{4}
$