6+40(2^2.7x)=206

Solution for 6+40(2^2.7x)=206 equation:

6+40(2^2.7x)=206

We move all terms to the left:

6+40(2^2.7x)-(206)=0

We add all the numbers together, and all the variables

40(2^2.7x)-200=0

We multiply parentheses

80x^2-200=0

a = 80; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·80·(-200)
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*80}=\frac{0-80\sqrt{10}}{160}
=-\frac{80\sqrt{10}}{160}
=-\frac{\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*80}=\frac{0+80\sqrt{10}}{160}
=\frac{80\sqrt{10}}{160}
=\frac{\sqrt{10}}{2}
$