11/12a-3/4a=-5/6

Solution for 11/12a-3/4a=-5/6 equation:

11/12a-3/4a=-5/6

We move all terms to the left:

11/12a-3/4a-(-5/6)=0


Domain of the equation: 12a!=0

a!=0/12

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

11/12a-3/4a+5/6=0

We calculate fractions


960a^2/1728a^2+1584a/1728a^2+(-1296a)/1728a^2=0

We multiply all the terms by the denominator


960a^2+1584a+(-1296a)=0

We get rid of parentheses

960a^2+1584a-1296a=0

We add all the numbers together, and all the variables

960a^2+288a=0

a = 960; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·960·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*960}=\frac{-576}{1920}
=-3/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*960}=\frac{0}{1920}
=0
$