-3/5x+1+3/10x=-2

Solution for -3/5x+1+3/10x=-2 equation:

-3/5x+1+3/10x=-2

We move all terms to the left:

-3/5x+1+3/10x-(-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(-30x)/50x^2+15x/50x^2+3=0

We multiply all the terms by the denominator


(-30x)+15x+3*50x^2=0

We add all the numbers together, and all the variables

15x+(-30x)+3*50x^2=0

Wy multiply elements

150x^2+15x+(-30x)=0

We get rid of parentheses

150x^2+15x-30x=0

We add all the numbers together, and all the variables

150x^2-15x=0

a = 150; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·150·0
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*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*150}=\frac{30}{300}
=1/10
$