2^x*x-6x=128

Solution for 2^x*x-6x=128 equation:

2^x*x-6x=128

We move all terms to the left:

2^x*x-6x-(128)=0

We add all the numbers together, and all the variables

-6x+2^x*x-128=0

Wy multiply elements

2x^2-6x-128=0

a = 2; b = -6; c = -128;
Δ = b2-4ac
Δ = -62-4·2·(-128)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{265}}{2*2}=\frac{6-2\sqrt{265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{265}}{2*2}=\frac{6+2\sqrt{265}}{4}
$