1/7x+7=1+2x

Solution for 1/7x+7=1+2x equation:

1/7x+7=1+2x

We move all terms to the left:

1/7x+7-(1+2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(2x+1)+7=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-14x^2-7x+49x+1=0

We add all the numbers together, and all the variables

-14x^2+42x+1=0

a = -14; b = 42; c = +1;
Δ = b2-4ac
Δ = 422-4·(-14)·1
Δ = 1820
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:

$\sqrt{\Delta}=\sqrt{1820}=\sqrt{4*455}=\sqrt{4}*\sqrt{455}=2\sqrt{455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{455}}{2*-14}=\frac{-42-2\sqrt{455}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{455}}{2*-14}=\frac{-42+2\sqrt{455}}{-28}
$