2/5a-3=3/10a-2

Solution for 2/5a-3=3/10a-2 equation:

2/5a-3=3/10a-2

We move all terms to the left:

2/5a-3-(3/10a-2)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 10a-2)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


20a+(-15a)-1*50a^2=0

Wy multiply elements

-50a^2+20a+(-15a)=0

We get rid of parentheses

-50a^2+20a-15a=0

We add all the numbers together, and all the variables

-50a^2+5a=0

a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-50}=\frac{-10}{-100}
=1/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-50}=\frac{0}{-100}
=0
$