2/7x-x=100

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

2/7x-x=100

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/7x-100=0

We multiply all the terms by the denominator


-1x*7x-100*7x+2=0

Wy multiply elements

-7x^2-700x+2=0

a = -7; b = -700; c = +2;
Δ = b2-4ac
Δ = -7002-4·(-7)·2
Δ = 490056
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:

$\sqrt{\Delta}=\sqrt{490056}=\sqrt{4*122514}=\sqrt{4}*\sqrt{122514}=2\sqrt{122514}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122514}}{2*-7}=\frac{700-2\sqrt{122514}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122514}}{2*-7}=\frac{700+2\sqrt{122514}}{-14}
$