5/7x+x=-3

Solution for 5/7x+x=-3 equation:

5/7x+x=-3

We move all terms to the left:

5/7x+x-(-3)=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+5/7x+3=0

We multiply all the terms by the denominator


x*7x+3*7x+5=0

Wy multiply elements

7x^2+21x+5=0

a = 7; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·7·5
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{301}}{2*7}=\frac{-21-\sqrt{301}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{301}}{2*7}=\frac{-21+\sqrt{301}}{14}
$