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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-20x)/50x^2+(-15x)/50x^2+3+1=0

We add all the numbers together, and all the variables

(-20x)/50x^2+(-15x)/50x^2+4=0

We multiply all the terms by the denominator


(-20x)+(-15x)+4*50x^2=0

Wy multiply elements

200x^2+(-20x)+(-15x)=0

We get rid of parentheses

200x^2-20x-15x=0

We add all the numbers together, and all the variables

200x^2-35x=0

a = 200; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·200·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*200}=\frac{0}{400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*200}=\frac{70}{400}
=7/40
$