7/15a+4/5a+13/10=11/5

Solution for 7/15a+4/5a+13/10=11/5 equation:

7/15a+4/5a+13/10=11/5

We move all terms to the left:

7/15a+4/5a+13/10-(11/5)=0


Domain of the equation: 15a!=0

a!=0/15

a!=0

a∈R



Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

7/15a+4/5a+13/10-(+11/5)=0

We get rid of parentheses

7/15a+4/5a+13/10-11/5=0

We calculate fractions


24375a^2/3750a^2+1750a/3750a^2+600a/3750a^2+(-1650a)/3750a^2=0

We multiply all the terms by the denominator


24375a^2+1750a+600a+(-1650a)=0

We add all the numbers together, and all the variables

24375a^2+2350a+(-1650a)=0

We get rid of parentheses

24375a^2+2350a-1650a=0

We add all the numbers together, and all the variables

24375a^2+700a=0

a = 24375; b = 700; c = 0;
Δ = b2-4ac
Δ = 7002-4·24375·0
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-700}{2*24375}=\frac{-1400}{48750}
=-28/975
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+700}{2*24375}=\frac{0}{48750}
=0
$