3/(7x)+1/4x=57

Solution for 3/(7x)+1/4x=57 equation:

3/(7x)+1/4x=57

We move all terms to the left:

3/(7x)+1/4x-(57)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


12x/28x^2+7x/28x^2-57=0

We multiply all the terms by the denominator


12x+7x-57*28x^2=0

We add all the numbers together, and all the variables

19x-57*28x^2=0

Wy multiply elements

-1596x^2+19x=0

a = -1596; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1596)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1596}=\frac{-38}{-3192}
=1/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1596}=\frac{0}{-3192}
=0
$