7x-1/2x=100/2-9

Solution for 7x-1/2x=100/2-9 equation:

7x-1/2x=100/2-9

We move all terms to the left:

7x-1/2x-(100/2-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7x-1/2x-41=0

We multiply all the terms by the denominator


7x*2x-41*2x-1=0

Wy multiply elements

14x^2-82x-1=0

a = 14; b = -82; c = -1;
Δ = b2-4ac
Δ = -822-4·14·(-1)
Δ = 6780
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:

$\sqrt{\Delta}=\sqrt{6780}=\sqrt{4*1695}=\sqrt{4}*\sqrt{1695}=2\sqrt{1695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1695}}{2*14}=\frac{82-2\sqrt{1695}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1695}}{2*14}=\frac{82+2\sqrt{1695}}{28}
$