7/4x+5/14x=39

Solution for 7/4x+5/14x=39 equation:

7/4x+5/14x=39

We move all terms to the left:

7/4x+5/14x-(39)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We calculate fractions


98x/56x^2+20x/56x^2-39=0

We multiply all the terms by the denominator


98x+20x-39*56x^2=0

We add all the numbers together, and all the variables

118x-39*56x^2=0

Wy multiply elements

-2184x^2+118x=0

a = -2184; b = 118; c = 0;
Δ = b2-4ac
Δ = 1182-4·(-2184)·0
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-118}{2*-2184}=\frac{-236}{-4368}
=59/1092
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+118}{2*-2184}=\frac{0}{-4368}
=0
$