100000=500*2^(2x)

Solution for 100000=500*2^(2x) equation:

100000=500*2^(2x)

We move all terms to the left:

100000-(500*2^(2x))=0

We get rid of parentheses

-500*2^2x+100000=0

Wy multiply elements

-1000x^2+100000=0

a = -1000; b = 0; c = +100000;
Δ = b2-4ac
Δ = 02-4·(-1000)·100000
Δ = 400000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400000000}=20000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20000}{2*-1000}=\frac{-20000}{-2000}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20000}{2*-1000}=\frac{20000}{-2000}
=-10
$