5/7x+1/4x=54

Solution for 5/7x+1/4x=54 equation:

5/7x+1/4x=54

We move all terms to the left:

5/7x+1/4x-(54)=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


20x/28x^2+7x/28x^2-54=0

We multiply all the terms by the denominator


20x+7x-54*28x^2=0

We add all the numbers together, and all the variables

27x-54*28x^2=0

Wy multiply elements

-1512x^2+27x=0

a = -1512; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-1512)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-1512}=\frac{-54}{-3024}
=1/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-1512}=\frac{0}{-3024}
=0
$