x+(-2/7x)=100

Solution for x+(-2/7x)=100 equation:

x+(-2/7x)=100

We move all terms to the left:

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


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x-2/7x-100=0

We multiply all the terms by the denominator


x*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}
$