4/7x+1/4x=54

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

4/7x+1/4x=54

We move all terms to the left:

4/7x+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


16x/28x^2+7x/28x^2-54=0

We multiply all the terms by the denominator


16x+7x-54*28x^2=0

We add all the numbers together, and all the variables

23x-54*28x^2=0

Wy multiply elements

-1512x^2+23x=0

a = -1512; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-1512)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-1512}=\frac{-46}{-3024}
=23/1512
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-1512}=\frac{0}{-3024}
=0
$