5/6a-7/12+3/4a=-13/6

Solution for 5/6a-7/12+3/4a=-13/6 equation:

5/6a-7/12+3/4a=-13/6

We move all terms to the left:

5/6a-7/12+3/4a-(-13/6)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

5/6a+3/4a-7/12+13/6=0

We calculate fractions


(-4032a^2)/1728a^2+240a/1728a^2+1296a/1728a^2+624a/1728a^2=0

We multiply all the terms by the denominator


(-4032a^2)+240a+1296a+624a=0

We add all the numbers together, and all the variables

(-4032a^2)+2160a=0

We get rid of parentheses

-4032a^2+2160a=0

a = -4032; b = 2160; c = 0;
Δ = b2-4ac
Δ = 21602-4·(-4032)·0
Δ = 4665600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4665600}=2160$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2160)-2160}{2*-4032}=\frac{-4320}{-8064}
=15/28
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2160)+2160}{2*-4032}=\frac{0}{-8064}
=0
$