x-2/7x=14

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

x-2/7x=14

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-14*7x-2=0

Wy multiply elements

7x^2-98x-2=0

a = 7; b = -98; c = -2;
Δ = b2-4ac
Δ = -982-4·7·(-2)
Δ = 9660
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:

$\sqrt{\Delta}=\sqrt{9660}=\sqrt{4*2415}=\sqrt{4}*\sqrt{2415}=2\sqrt{2415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2415}}{2*7}=\frac{98-2\sqrt{2415}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2415}}{2*7}=\frac{98+2\sqrt{2415}}{14}
$