12/5x+6=3/20x

Solution for 12/5x+6=3/20x equation:

12/5x+6=3/20x

We move all terms to the left:

12/5x+6-(3/20x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12/5x-(+3/20x)+6=0

We get rid of parentheses

12/5x-3/20x+6=0

We calculate fractions


240x/100x^2+(-15x)/100x^2+6=0

We multiply all the terms by the denominator


240x+(-15x)+6*100x^2=0

Wy multiply elements

600x^2+240x+(-15x)=0

We get rid of parentheses

600x^2+240x-15x=0

We add all the numbers together, and all the variables

600x^2+225x=0

a = 600; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·600·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*600}=\frac{-450}{1200}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*600}=\frac{0}{1200}
=0
$