15x^2-2=25

Solution for 15x^2-2=25 equation:

15x^2-2=25

We move all terms to the left:

15x^2-2-(25)=0

We add all the numbers together, and all the variables

15x^2-27=0

a = 15; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·15·(-27)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{5}}{2*15}=\frac{0-18\sqrt{5}}{30}
=-\frac{18\sqrt{5}}{30}
=-\frac{3\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{5}}{2*15}=\frac{0+18\sqrt{5}}{30}
=\frac{18\sqrt{5}}{30}
=\frac{3\sqrt{5}}{5}
$