2.5(5^2x-1)=30

Solution for 2.5(5^2x-1)=30 equation:

2.5(5^2x-1)=30

We move all terms to the left:

2.5(5^2x-1)-(30)=0

We multiply parentheses

12.5x^2-2.5-30=0

We add all the numbers together, and all the variables

12.5x^2-32.5=0

a = 12.5; b = 0; c = -32.5;
Δ = b2-4ac
Δ = 02-4·12.5·(-32.5)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{65}}{2*12.5}=\frac{0-5\sqrt{65}}{25}
=-\frac{5\sqrt{65}}{25}
=-\frac{\sqrt{65}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{65}}{2*12.5}=\frac{0+5\sqrt{65}}{25}
=\frac{5\sqrt{65}}{25}
=\frac{\sqrt{65}}{5}
$