a=58a-a^2+6

Solution for a=58a-a^2+6 equation:

a=58a-a^2+6

We move all terms to the left:

a-(58a-a^2+6)=0

We get rid of parentheses

a^2-58a+a-6=0

We add all the numbers together, and all the variables

a^2-57a-6=0

a = 1; b = -57; c = -6;
Δ = b2-4ac
Δ = -572-4·1·(-6)
Δ = 3273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-\sqrt{3273}}{2*1}=\frac{57-\sqrt{3273}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{3273}}{2*1}=\frac{57+\sqrt{3273}}{2}
$