3/10x-4=3/5x

Solution for 3/10x-4=3/5x equation:

3/10x-4=3/5x

We move all terms to the left:

3/10x-4-(3/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/10x-(+3/5x)-4=0

We get rid of parentheses

3/10x-3/5x-4=0

We calculate fractions


15x/50x^2+(-30x)/50x^2-4=0

We multiply all the terms by the denominator


15x+(-30x)-4*50x^2=0

Wy multiply elements

-200x^2+15x+(-30x)=0

We get rid of parentheses

-200x^2+15x-30x=0

We add all the numbers together, and all the variables

-200x^2-15x=0

a = -200; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-200)·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*-200}=\frac{0}{-400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-200}=\frac{30}{-400}
=-3/40
$