(20x+50)2x=25200

Solution for (20x+50)2x=25200 equation:

(20x+50)2x=25200

We move all terms to the left:

(20x+50)2x-(25200)=0

We multiply parentheses

40x^2+100x-25200=0

a = 40; b = 100; c = -25200;
Δ = b2-4ac
Δ = 1002-4·40·(-25200)
Δ = 4042000
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:

$\sqrt{\Delta}=\sqrt{4042000}=\sqrt{400*10105}=\sqrt{400}*\sqrt{10105}=20\sqrt{10105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{10105}}{2*40}=\frac{-100-20\sqrt{10105}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{10105}}{2*40}=\frac{-100+20\sqrt{10105}}{80}
$