2x+1/2x+3=105

Solution for 2x+1/2x+3=105 equation:

2x+1/2x+3=105

We move all terms to the left:

2x+1/2x+3-(105)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-102=0

We multiply all the terms by the denominator


2x*2x-102*2x+1=0

Wy multiply elements

4x^2-204x+1=0

a = 4; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·4·1
Δ = 41600
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:

$\sqrt{\Delta}=\sqrt{41600}=\sqrt{1600*26}=\sqrt{1600}*\sqrt{26}=40\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-40\sqrt{26}}{2*4}=\frac{204-40\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+40\sqrt{26}}{2*4}=\frac{204+40\sqrt{26}}{8}
$