4x+1/2x=81

Solution for 4x+1/2x=81 equation:

4x+1/2x=81

We move all terms to the left:

4x+1/2x-(81)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-81*2x+1=0

Wy multiply elements

8x^2-162x+1=0

a = 8; b = -162; c = +1;
Δ = b2-4ac
Δ = -1622-4·8·1
Δ = 26212
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:

$\sqrt{\Delta}=\sqrt{26212}=\sqrt{4*6553}=\sqrt{4}*\sqrt{6553}=2\sqrt{6553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6553}}{2*8}=\frac{162-2\sqrt{6553}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6553}}{2*8}=\frac{162+2\sqrt{6553}}{16}
$