2^2x=4/7

Solution for 2^2x=4/7 equation:

2^2x=4/7

We move all terms to the left:

2^2x-(4/7)=0

We add all the numbers together, and all the variables

2^2x-(+4/7)=0

We get rid of parentheses

2^2x-4/7=0

We multiply all the terms by the denominator


2^2x*7-4=0

Wy multiply elements

14x^2-4=0

a = 14; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·14·(-4)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*14}=\frac{0-4\sqrt{14}}{28}
=-\frac{4\sqrt{14}}{28}
=-\frac{\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*14}=\frac{0+4\sqrt{14}}{28}
=\frac{4\sqrt{14}}{28}
=\frac{\sqrt{14}}{7}
$