4/x+4=15/4x

Solution for 4/x+4=15/4x equation:

4/x+4=15/4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/x-15/4x+4=0

We calculate fractions


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

We multiply all the terms by the denominator


16x+(-15x)+4*4x^2=0

Wy multiply elements

16x^2+16x+(-15x)=0

We get rid of parentheses

16x^2+16x-15x=0

We add all the numbers together, and all the variables

16x^2+x=0

a = 16; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·16·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*16}=\frac{-2}{32}
=-1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*16}=\frac{0}{32}
=0
$