(3+x)2x=150

Solution for (3+x)2x=150 equation:

(3+x)2x=150

We move all terms to the left:

(3+x)2x-(150)=0

We add all the numbers together, and all the variables

(x+3)2x-150=0

We multiply parentheses

2x^2+6x-150=0

a = 2; b = 6; c = -150;
Δ = b2-4ac
Δ = 62-4·2·(-150)
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{309}}{2*2}=\frac{-6-2\sqrt{309}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{309}}{2*2}=\frac{-6+2\sqrt{309}}{4}
$