1/x+1/4x=1/15

Solution for 1/x+1/4x=1/15 equation:

1/x+1/4x=1/15

We move all terms to the left:

1/x+1/4x-(1/15)=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

1/x+1/4x-(+1/15)=0

We get rid of parentheses

1/x+1/4x-1/15=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

(-16x^2)+75x=0

We get rid of parentheses

-16x^2+75x=0

a = -16; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-16)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-16}=\frac{-150}{-32}
=4+11/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-16}=\frac{0}{-32}
=0
$