8x(6-2x)=34

Solution for 8x(6-2x)=34 equation:

8x(6-2x)=34

We move all terms to the left:

8x(6-2x)-(34)=0

We add all the numbers together, and all the variables

8x(-2x+6)-34=0

We multiply parentheses

-16x^2+48x-34=0

a = -16; b = 48; c = -34;
Δ = b2-4ac
Δ = 482-4·(-16)·(-34)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{2}}{2*-16}=\frac{-48-8\sqrt{2}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{2}}{2*-16}=\frac{-48+8\sqrt{2}}{-32}
$