7-2x/2x-2x+1/14x=1

Solution for 7-2x/2x-2x+1/14x=1 equation:

7-2x/2x-2x+1/14x=1

We move all terms to the left:

7-2x/2x-2x+1/14x-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-2x/2x+1/14x+6=0

Fractions to decimals

1/14x-2x+6+1=0

We multiply all the terms by the denominator


-2x*14x+6*14x+1*14x+1=0

Wy multiply elements

-28x^2+84x+14x+1=0

We add all the numbers together, and all the variables

-28x^2+98x+1=0

a = -28; b = 98; c = +1;
Δ = b2-4ac
Δ = 982-4·(-28)·1
Δ = 9716
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:

$\sqrt{\Delta}=\sqrt{9716}=\sqrt{4*2429}=\sqrt{4}*\sqrt{2429}=2\sqrt{2429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{2429}}{2*-28}=\frac{-98-2\sqrt{2429}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{2429}}{2*-28}=\frac{-98+2\sqrt{2429}}{-56}
$