2(5x-2)2x-2=34

Solution for 2(5x-2)2x-2=34 equation:

2(5x-2)2x-2=34

We move all terms to the left:

2(5x-2)2x-2-(34)=0

We add all the numbers together, and all the variables

2(5x-2)2x-36=0

We multiply parentheses

20x^2-8x-36=0

a = 20; b = -8; c = -36;
Δ = b2-4ac
Δ = -82-4·20·(-36)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{46}}{2*20}=\frac{8-8\sqrt{46}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{46}}{2*20}=\frac{8+8\sqrt{46}}{40}
$