3(5^2x-1)-2=373

Solution for 3(5^2x-1)-2=373 equation:

3(5^2x-1)-2=373

We move all terms to the left:

3(5^2x-1)-2-(373)=0

We add all the numbers together, and all the variables

3(5^2x-1)-375=0

We multiply parentheses

15x^2-3-375=0

We add all the numbers together, and all the variables

15x^2-378=0

a = 15; b = 0; c = -378;
Δ = b2-4ac
Δ = 02-4·15·(-378)
Δ = 22680
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:

$\sqrt{\Delta}=\sqrt{22680}=\sqrt{324*70}=\sqrt{324}*\sqrt{70}=18\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{70}}{2*15}=\frac{0-18\sqrt{70}}{30}
=-\frac{18\sqrt{70}}{30}
=-\frac{3\sqrt{70}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{70}}{2*15}=\frac{0+18\sqrt{70}}{30}
=\frac{18\sqrt{70}}{30}
=\frac{3\sqrt{70}}{5}
$