4/x=16/15x+4

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

4/x=16/15x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 15x+4)!=0

x∈R


We get rid of parentheses

4/x-16/15x-4=0

We calculate fractions


60x/15x^2+(-16x)/15x^2-4=0

We multiply all the terms by the denominator


60x+(-16x)-4*15x^2=0

Wy multiply elements

-60x^2+60x+(-16x)=0

We get rid of parentheses

-60x^2+60x-16x=0

We add all the numbers together, and all the variables

-60x^2+44x=0

a = -60; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-60)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-60}=\frac{-88}{-120}
=11/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-60}=\frac{0}{-120}
=0
$