(3x+5)2x=2600

Solution for (3x+5)2x=2600 equation:

(3x+5)2x=2600

We move all terms to the left:

(3x+5)2x-(2600)=0

We multiply parentheses

6x^2+10x-2600=0

a = 6; b = 10; c = -2600;
Δ = b2-4ac
Δ = 102-4·6·(-2600)
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-250}{2*6}=\frac{-260}{12}
=-21+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+250}{2*6}=\frac{240}{12}
=20
$