4^x=3/4x+2

Solution for 4^x=3/4x+2 equation:

4^x=3/4x+2

We move all terms to the left:

4^x-(3/4x+2)=0


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-8x-3=0

a = 16; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·16·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*16}=\frac{-8}{32}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*16}=\frac{24}{32}
=3/4
$