2x+3=1/2x+105

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

2x+3=1/2x+105

We move all terms to the left:

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


Domain of the equation: 2x+105)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x-105*2x+3*2x-1=0

Wy multiply elements

4x^2-210x+6x-1=0

We add all the numbers together, and all the variables

4x^2-204x-1=0

a = 4; b = -204; c = -1;
Δ = b2-4ac
Δ = -2042-4·4·(-1)
Δ = 41632
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:

$\sqrt{\Delta}=\sqrt{41632}=\sqrt{16*2602}=\sqrt{16}*\sqrt{2602}=4\sqrt{2602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-4\sqrt{2602}}{2*4}=\frac{204-4\sqrt{2602}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+4\sqrt{2602}}{2*4}=\frac{204+4\sqrt{2602}}{8}
$