5/6a+4=2/3a+6

Solution for 5/6a+4=2/3a+6 equation:

5/6a+4=2/3a+6

We move all terms to the left:

5/6a+4-(2/3a+6)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R



Domain of the equation: 3a+6)!=0

a∈R


We get rid of parentheses

5/6a-2/3a-6+4=0

We calculate fractions


15a/18a^2+(-12a)/18a^2-6+4=0

We add all the numbers together, and all the variables

15a/18a^2+(-12a)/18a^2-2=0

We multiply all the terms by the denominator


15a+(-12a)-2*18a^2=0

Wy multiply elements

-36a^2+15a+(-12a)=0

We get rid of parentheses

-36a^2+15a-12a=0

We add all the numbers together, and all the variables

-36a^2+3a=0

a = -36; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-36)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-36}=\frac{-6}{-72}
=1/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-36}=\frac{0}{-72}
=0
$