8/x=1/2x+60

Solution for 8/x=1/2x+60 equation:

8/x=1/2x+60

We move all terms to the left:

8/x-(1/2x+60)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+60)!=0

x∈R


We get rid of parentheses

8/x-1/2x-60=0

We calculate fractions


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

We add all the numbers together, and all the variables

16x/2x^2+(-1x)/2x^2-60=0

We multiply all the terms by the denominator


16x+(-1x)-60*2x^2=0

Wy multiply elements

-120x^2+16x+(-1x)=0

We get rid of parentheses

-120x^2+16x-1x=0

We add all the numbers together, and all the variables

-120x^2+15x=0

a = -120; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-120)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-120}=\frac{-30}{-240}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-120}=\frac{0}{-240}
=0
$