2x+2+7+x+1/2x=75

Solution for 2x+2+7+x+1/2x=75 equation:

2x+2+7+x+1/2x=75

We move all terms to the left:

2x+2+7+x+1/2x-(75)=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-66=0

We multiply all the terms by the denominator


3x*2x-66*2x+1=0

Wy multiply elements

6x^2-132x+1=0

a = 6; b = -132; c = +1;
Δ = b2-4ac
Δ = -1322-4·6·1
Δ = 17400
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:

$\sqrt{\Delta}=\sqrt{17400}=\sqrt{100*174}=\sqrt{100}*\sqrt{174}=10\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-10\sqrt{174}}{2*6}=\frac{132-10\sqrt{174}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+10\sqrt{174}}{2*6}=\frac{132+10\sqrt{174}}{12}
$