2/x+1-6/7x+7=5

Solution for 2/x+1-6/7x+7=5 equation:

2/x+1-6/7x+7=5

We move all terms to the left:

2/x+1-6/7x+7-(5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-6/7x+3=0

We calculate fractions


14x/7x^2+(-6x)/7x^2+3=0

We multiply all the terms by the denominator


14x+(-6x)+3*7x^2=0

Wy multiply elements

21x^2+14x+(-6x)=0

We get rid of parentheses

21x^2+14x-6x=0

We add all the numbers together, and all the variables

21x^2+8x=0

a = 21; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·21·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*21}=\frac{-16}{42}
=-8/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*21}=\frac{0}{42}
=0
$