4^x-1=3/3x

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

4^x-1=3/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4^x-(+3/3x)-1=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-3x-3=0

a = 12; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·12·(-3)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*12}=\frac{3-3\sqrt{17}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*12}=\frac{3+3\sqrt{17}}{24}
$