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

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 = 489944
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:

$\sqrt{\Delta}=\sqrt{489944}=\sqrt{4*122486}=\sqrt{4}*\sqrt{122486}=2\sqrt{122486}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122486}}{2*7}=\frac{700-2\sqrt{122486}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122486}}{2*7}=\frac{700+2\sqrt{122486}}{14}
$