25=11*10^(2x)

Solution for 25=11*10^(2x) equation:

25=11*10^(2x)

We move all terms to the left:

25-(11*10^(2x))=0

We get rid of parentheses

-11*10^2x+25=0

Wy multiply elements

-110x^2+25=0

a = -110; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-110)·25
Δ = 11000
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:

$\sqrt{\Delta}=\sqrt{11000}=\sqrt{100*110}=\sqrt{100}*\sqrt{110}=10\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{110}}{2*-110}=\frac{0-10\sqrt{110}}{-220}
=-\frac{10\sqrt{110}}{-220}
=-\frac{\sqrt{110}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{110}}{2*-110}=\frac{0+10\sqrt{110}}{-220}
=\frac{10\sqrt{110}}{-220}
=\frac{\sqrt{110}}{-22}
$