4/x+4-2/4x+16=15

Solution for 4/x+4-2/4x+16=15 equation:

4/x+4-2/4x+16=15

We move all terms to the left:

4/x+4-2/4x+16-(15)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-2/4x+5=0

We calculate fractions


16x/4x^2+(-2x)/4x^2+5=0

We multiply all the terms by the denominator


16x+(-2x)+5*4x^2=0

Wy multiply elements

20x^2+16x+(-2x)=0

We get rid of parentheses

20x^2+16x-2x=0

We add all the numbers together, and all the variables

20x^2+14x=0

a = 20; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·20·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*20}=\frac{-28}{40}
=-7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*20}=\frac{0}{40}
=0
$