2+3^4-5/6*a=a

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

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

We move all terms to the left:

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


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

-1a-5/6a+83=0

We multiply all the terms by the denominator


-1a*6a+83*6a-5=0

Wy multiply elements

-6a^2+498a-5=0

a = -6; b = 498; c = -5;
Δ = b2-4ac
Δ = 4982-4·(-6)·(-5)
Δ = 247884
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:

$\sqrt{\Delta}=\sqrt{247884}=\sqrt{4*61971}=\sqrt{4}*\sqrt{61971}=2\sqrt{61971}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(498)-2\sqrt{61971}}{2*-6}=\frac{-498-2\sqrt{61971}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(498)+2\sqrt{61971}}{2*-6}=\frac{-498+2\sqrt{61971}}{-12}
$