2/3a-1/5a=2

Solution for 2/3a-1/5a=2 equation:

2/3a-1/5a=2

We move all terms to the left:

2/3a-1/5a-(2)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We calculate fractions


10a/15a^2+(-3a)/15a^2-2=0

We multiply all the terms by the denominator


10a+(-3a)-2*15a^2=0

Wy multiply elements

-30a^2+10a+(-3a)=0

We get rid of parentheses

-30a^2+10a-3a=0

We add all the numbers together, and all the variables

-30a^2+7a=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60}
=7/30
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$