2^x=1/2x+14

Solution for 2^x=1/2x+14 equation:

2^x=1/2x+14

We move all terms to the left:

2^x-(1/2x+14)=0


Domain of the equation: 2x+14)!=0

x∈R


We get rid of parentheses

2^x-1/2x-14=0

We multiply all the terms by the denominator


2^x*2x-14*2x-1=0

Wy multiply elements

4x^2-28x-1=0

a = 4; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·4·(-1)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20\sqrt{2}}{2*4}=\frac{28-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20\sqrt{2}}{2*4}=\frac{28+20\sqrt{2}}{8}
$