3/5x-1=-3/10x

Solution for 3/5x-1=-3/10x equation:

3/5x-1=-3/10x

We move all terms to the left:

3/5x-1-(-3/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3/5x+3/10x-1=0

We calculate fractions


30x/50x^2+15x/50x^2-1=0

We multiply all the terms by the denominator


30x+15x-1*50x^2=0

We add all the numbers together, and all the variables

45x-1*50x^2=0

Wy multiply elements

-50x^2+45x=0

a = -50; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-50)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-50}=\frac{-90}{-100}
=9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-50}=\frac{0}{-100}
=0
$