27x^2-64=0

Solution for 27x^2-64=0 equation:

27x^2-64=0

a = 27; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·27·(-64)
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*27}=\frac{0-48\sqrt{3}}{54}
=-\frac{48\sqrt{3}}{54}
=-\frac{8\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*27}=\frac{0+48\sqrt{3}}{54}
=\frac{48\sqrt{3}}{54}
=\frac{8\sqrt{3}}{9}
$