1/4a-4/9+5/6a=2/9

Solution for 1/4a-4/9+5/6a=2/9 equation:

1/4a-4/9+5/6a=2/9

We move all terms to the left:

1/4a-4/9+5/6a-(2/9)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

1/4a+5/6a-4/9-(+2/9)=0

We get rid of parentheses

1/4a+5/6a-4/9-2/9=0

We calculate fractions


(-288a^2-4)/1944a^2+486a/1944a^2+1620a/1944a^2=0

We multiply all the terms by the denominator


(-288a^2-4)+486a+1620a=0

We add all the numbers together, and all the variables

(-288a^2-4)+2106a=0

We get rid of parentheses

-288a^2+2106a-4=0

a = -288; b = 2106; c = -4;
Δ = b2-4ac
Δ = 21062-4·(-288)·(-4)
Δ = 4430628
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4430628}=\sqrt{36*123073}=\sqrt{36}*\sqrt{123073}=6\sqrt{123073}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2106)-6\sqrt{123073}}{2*-288}=\frac{-2106-6\sqrt{123073}}{-576}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2106)+6\sqrt{123073}}{2*-288}=\frac{-2106+6\sqrt{123073}}{-576}
$