3x+1/2x=22

Solution for 3x+1/2x=22 equation:

3x+1/2x=22

We move all terms to the left:

3x+1/2x-(22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-22*2x+1=0

Wy multiply elements

6x^2-44x+1=0

a = 6; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·6·1
Δ = 1912
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:

$\sqrt{\Delta}=\sqrt{1912}=\sqrt{4*478}=\sqrt{4}*\sqrt{478}=2\sqrt{478}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{478}}{2*6}=\frac{44-2\sqrt{478}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{478}}{2*6}=\frac{44+2\sqrt{478}}{12}
$