(4/x+4)-2/7=1/4x+16

Solution for (4/x+4)-2/7=1/4x+16 equation:

(4/x+4)-2/7=1/4x+16

We move all terms to the left:

(4/x+4)-2/7-(1/4x+16)=0


Domain of the equation: x+4)!=0

x∈R



Domain of the equation: 4x+16)!=0

x∈R


We get rid of parentheses

4/x-1/4x+4-16-2/7=0

We calculate fractions


(-32x^2)/196x^2+784x/196x^2+(-49x)/196x^2+4-16=0

We add all the numbers together, and all the variables

(-32x^2)/196x^2+784x/196x^2+(-49x)/196x^2-12=0

We multiply all the terms by the denominator


(-32x^2)+784x+(-49x)-12*196x^2=0

Wy multiply elements

(-32x^2)-2352x^2+784x+(-49x)=0

We get rid of parentheses

-32x^2-2352x^2+784x-49x=0

We add all the numbers together, and all the variables

-2384x^2+735x=0

a = -2384; b = 735; c = 0;
Δ = b2-4ac
Δ = 7352-4·(-2384)·0
Δ = 540225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540225}=735$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(735)-735}{2*-2384}=\frac{-1470}{-4768}
=735/2384
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(735)+735}{2*-2384}=\frac{0}{-4768}
=0
$