X+1/2x+2x-7=2101

Solution for X+1/2x+2x-7=2101 equation:

X+1/2X+2X-7=2101

We move all terms to the left:

X+1/2X+2X-7-(2101)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/2X-2108=0

We multiply all the terms by the denominator


3X*2X-2108*2X+1=0

Wy multiply elements

6X^2-4216X+1=0

a = 6; b = -4216; c = +1;
Δ = b2-4ac
Δ = -42162-4·6·1
Δ = 17774632
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:

$\sqrt{\Delta}=\sqrt{17774632}=\sqrt{4*4443658}=\sqrt{4}*\sqrt{4443658}=2\sqrt{4443658}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4216)-2\sqrt{4443658}}{2*6}=\frac{4216-2\sqrt{4443658}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4216)+2\sqrt{4443658}}{2*6}=\frac{4216+2\sqrt{4443658}}{12}
$