2+3x+2/7x=-21

Solution for 2+3x+2/7x=-21 equation:

2+3x+2/7x=-21

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/7x+23=0

We multiply all the terms by the denominator


3x*7x+23*7x+2=0

Wy multiply elements

21x^2+161x+2=0

a = 21; b = 161; c = +2;
Δ = b2-4ac
Δ = 1612-4·21·2
Δ = 25753
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{-(161)-\sqrt{25753}}{2*21}=\frac{-161-\sqrt{25753}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(161)+\sqrt{25753}}{2*21}=\frac{-161+\sqrt{25753}}{42}
$