2^(2x)=11/7

Solution for 2^(2x)=11/7 equation:

2^(2x)=11/7

We move all terms to the left:

2^(2x)-(11/7)=0

We add all the numbers together, and all the variables

2^2x-(+11/7)=0

We get rid of parentheses

2^2x-11/7=0

We multiply all the terms by the denominator


2^2x*7-11=0

Wy multiply elements

14x^2-11=0

a = 14; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·14·(-11)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{154}}{2*14}=\frac{0-2\sqrt{154}}{28}
=-\frac{2\sqrt{154}}{28}
=-\frac{\sqrt{154}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{154}}{2*14}=\frac{0+2\sqrt{154}}{28}
=\frac{2\sqrt{154}}{28}
=\frac{\sqrt{154}}{14}
$