3x/5x=60/8x

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

3x/5x=60/8x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


24x^2/40x^2+(-300x)/40x^2=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{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+300}{2*24}=\frac{600}{48}
=12+1/2
$