3/7x+1/2x=-1/14

Solution for 3/7x+1/2x=-1/14 equation:

3/7x+1/2x=-1/14

We move all terms to the left:

3/7x+1/2x-(-1/14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/7x+1/2x+1/14=0

We calculate fractions


28x^2/196x^2+84x/196x^2+98x/196x^2=0

We multiply all the terms by the denominator


28x^2+84x+98x=0

We add all the numbers together, and all the variables

28x^2+182x=0

a = 28; b = 182; c = 0;
Δ = b2-4ac
Δ = 1822-4·28·0
Δ = 33124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33124}=182$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(182)-182}{2*28}=\frac{-364}{56}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(182)+182}{2*28}=\frac{0}{56}
=0
$