27x^2-125=0

Solution for 27x^2-125=0 equation:

27x^2-125=0

a = 27; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·27·(-125)
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{15}}{2*27}=\frac{0-30\sqrt{15}}{54}
=-\frac{30\sqrt{15}}{54}
=-\frac{5\sqrt{15}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{15}}{2*27}=\frac{0+30\sqrt{15}}{54}
=\frac{30\sqrt{15}}{54}
=\frac{5\sqrt{15}}{9}
$