3/5x+2=2/10x+12

Solution for 3/5x+2=2/10x+12 equation:

3/5x+2=2/10x+12

We move all terms to the left:

3/5x+2-(2/10x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+12)!=0

x∈R


We get rid of parentheses

3/5x-2/10x-12+2=0

We calculate fractions


30x/50x^2+(-10x)/50x^2-12+2=0

We add all the numbers together, and all the variables

30x/50x^2+(-10x)/50x^2-10=0

We multiply all the terms by the denominator


30x+(-10x)-10*50x^2=0

Wy multiply elements

-500x^2+30x+(-10x)=0

We get rid of parentheses

-500x^2+30x-10x=0

We add all the numbers together, and all the variables

-500x^2+20x=0

a = -500; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-500)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-500}=\frac{-40}{-1000}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-500}=\frac{0}{-1000}
=0
$