94x+1/2x=44

Solution for 94x+1/2x=44 equation:

94x+1/2x=44

We move all terms to the left:

94x+1/2x-(44)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


94x*2x-44*2x+1=0

Wy multiply elements

188x^2-88x+1=0

a = 188; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·188·1
Δ = 6992
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:

$\sqrt{\Delta}=\sqrt{6992}=\sqrt{16*437}=\sqrt{16}*\sqrt{437}=4\sqrt{437}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{437}}{2*188}=\frac{88-4\sqrt{437}}{376}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{437}}{2*188}=\frac{88+4\sqrt{437}}{376}
$