1/4x-4=3/7x+6

Solution for 1/4x-4=3/7x+6 equation:

1/4x-4=3/7x+6

We move all terms to the left:

1/4x-4-(3/7x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x+6)!=0

x∈R


We get rid of parentheses

1/4x-3/7x-6-4=0

We calculate fractions


7x/28x^2+(-12x)/28x^2-6-4=0

We add all the numbers together, and all the variables

7x/28x^2+(-12x)/28x^2-10=0

We multiply all the terms by the denominator


7x+(-12x)-10*28x^2=0

Wy multiply elements

-280x^2+7x+(-12x)=0

We get rid of parentheses

-280x^2+7x-12x=0

We add all the numbers together, and all the variables

-280x^2-5x=0

a = -280; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-280)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-280}=\frac{0}{-560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-280}=\frac{10}{-560}
=-1/56
$