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

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

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

We move all terms to the left:

10/5x+3-(2/10x-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

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

We calculate fractions


100x/50x^2+(-10x)/50x^2+3+3=0

We add all the numbers together, and all the variables

100x/50x^2+(-10x)/50x^2+6=0

We multiply all the terms by the denominator


100x+(-10x)+6*50x^2=0

Wy multiply elements

300x^2+100x+(-10x)=0

We get rid of parentheses

300x^2+100x-10x=0

We add all the numbers together, and all the variables

300x^2+90x=0

a = 300; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·300·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*300}=\frac{-180}{600}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*300}=\frac{0}{600}
=0
$