3/x+1-3/7x+7=-6

Solution for 3/x+1-3/7x+7=-6 equation:

3/x+1-3/7x+7=-6

We move all terms to the left:

3/x+1-3/7x+7-(-6)=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

3/x-3/7x+14=0

We calculate fractions


21x/7x^2+(-3x)/7x^2+14=0

We multiply all the terms by the denominator


21x+(-3x)+14*7x^2=0

Wy multiply elements

98x^2+21x+(-3x)=0

We get rid of parentheses

98x^2+21x-3x=0

We add all the numbers together, and all the variables

98x^2+18x=0

a = 98; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·98·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*98}=\frac{-36}{196}
=-9/49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*98}=\frac{0}{196}
=0
$