-4/7x-9/28x+1/4=-54

Solution for -4/7x-9/28x+1/4=-54 equation:

-4/7x-9/28x+1/4=-54

We move all terms to the left:

-4/7x-9/28x+1/4-(-54)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We add all the numbers together, and all the variables

-4/7x-9/28x+54+1/4=0

We calculate fractions


392x^2/3136x^2+(-1792x)/3136x^2+(-1008x)/3136x^2+54=0

We multiply all the terms by the denominator


392x^2+(-1792x)+(-1008x)+54*3136x^2=0

Wy multiply elements

392x^2+169344x^2+(-1792x)+(-1008x)=0

We get rid of parentheses

392x^2+169344x^2-1792x-1008x=0

We add all the numbers together, and all the variables

169736x^2-2800x=0

a = 169736; b = -2800; c = 0;
Δ = b2-4ac
Δ = -28002-4·169736·0
Δ = 7840000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7840000}=2800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2800)-2800}{2*169736}=\frac{0}{339472}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2800)+2800}{2*169736}=\frac{5600}{339472}
=50/3031
$