6x+14/7x=-7

Solution for 6x+14/7x=-7 equation:

6x+14/7x=-7

We move all terms to the left:

6x+14/7x-(-7)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

6x+14/7x+7=0

We multiply all the terms by the denominator


6x*7x+7*7x+14=0

Wy multiply elements

42x^2+49x+14=0

a = 42; b = 49; c = +14;
Δ = b2-4ac
Δ = 492-4·42·14
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-7}{2*42}=\frac{-56}{84}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+7}{2*42}=\frac{-42}{84}
=-1/2
$