1/4^x-4=3*1/2^x

Solution for 1/4^x-4=3*1/2^x equation:

1/4^x-4=3*1/2^x

We move all terms to the left:

1/4^x-4-(3*1/2^x)=0


Domain of the equation: 4^x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/4^x-3*1/2^x-4=0

We calculate fractions


2x/8x^2+(-48x)/8x^2-4=0

We multiply all the terms by the denominator


2x+(-48x)-4*8x^2=0

Wy multiply elements

-32x^2+2x+(-48x)=0

We get rid of parentheses

-32x^2+2x-48x=0

We add all the numbers together, and all the variables

-32x^2-46x=0

a = -32; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·(-32)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*-32}=\frac{92}{-64}
=-1+7/16
$