-10/a+5/3a=35/6

Solution for -10/a+5/3a=35/6 equation:

-10/a+5/3a=35/6

We move all terms to the left:

-10/a+5/3a-(35/6)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

-10/a+5/3a-(+35/6)=0

We get rid of parentheses

-10/a+5/3a-35/6=0

We calculate fractions


(-315a^2)/108a^2+(-1080a)/108a^2+180a/108a^2=0

We multiply all the terms by the denominator


(-315a^2)+(-1080a)+180a=0

We add all the numbers together, and all the variables

(-315a^2)+180a+(-1080a)=0

We get rid of parentheses

-315a^2+180a-1080a=0

We add all the numbers together, and all the variables

-315a^2-900a=0

a = -315; b = -900; c = 0;
Δ = b2-4ac
Δ = -9002-4·(-315)·0
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-900}{2*-315}=\frac{0}{-630}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+900}{2*-315}=\frac{1800}{-630}
=-2+6/7
$