5x/8x=3x/60

Solution for 5x/8x=3x/60 equation:

5x/8x=3x/60

We move all terms to the left:

5x/8x-(3x/60)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5x/8x-(+3x/60)=0

We get rid of parentheses

5x/8x-3x/60=0

We calculate fractions


(-24x^2)/480x+300x/480x=0

We multiply all the terms by the denominator


(-24x^2)+300x=0

We get rid of parentheses

-24x^2+300x=0

a = -24; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-24)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-24}=\frac{-600}{-48}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-24}=\frac{0}{-48}
=0
$