3/2a-7/5a=-2/15

Solution for 3/2a-7/5a=-2/15 equation:

3/2a-7/5a=-2/15

We move all terms to the left:

3/2a-7/5a-(-2/15)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

3/2a-7/5a+2/15=0

We calculate fractions


100a^2/150a^2+225a/150a^2+(-210a)/150a^2=0

We multiply all the terms by the denominator


100a^2+225a+(-210a)=0

We get rid of parentheses

100a^2+225a-210a=0

We add all the numbers together, and all the variables

100a^2+15a=0

a = 100; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·100·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*100}=\frac{-30}{200}
=-3/20
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*100}=\frac{0}{200}
=0
$