x-1/7x=100

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

x-1/7x=100

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-100*7x-1=0

Wy multiply elements

7x^2-700x-1=0

a = 7; b = -700; c = -1;
Δ = b2-4ac
Δ = -7002-4·7·(-1)
Δ = 490028
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:

$\sqrt{\Delta}=\sqrt{490028}=\sqrt{4*122507}=\sqrt{4}*\sqrt{122507}=2\sqrt{122507}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122507}}{2*7}=\frac{700-2\sqrt{122507}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122507}}{2*7}=\frac{700+2\sqrt{122507}}{14}
$