2(2x+1)2x=50

Solution for 2(2x+1)2x=50 equation:

2(2x+1)2x=50

We move all terms to the left:

2(2x+1)2x-(50)=0

We multiply parentheses

8x^2+4x-50=0

a = 8; b = 4; c = -50;
Δ = b2-4ac
Δ = 42-4·8·(-50)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{101}}{2*8}=\frac{-4-4\sqrt{101}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{101}}{2*8}=\frac{-4+4\sqrt{101}}{16}
$