2^x=1/4x+3

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

2^x=1/4x+3

We move all terms to the left:

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


Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-12x-1=0

a = 8; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·8·(-1)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{11}}{2*8}=\frac{12-4\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*8}=\frac{12+4\sqrt{11}}{16}
$