57=a(2)-3

Solution for 57=a(2)-3 equation:

57=a(2)-3

We move all terms to the left:

57-(a(2)-3)=0

We add all the numbers together, and all the variables

-(+a^2-3)+57=0

We get rid of parentheses

-a^2+3+57=0

We add all the numbers together, and all the variables

-1a^2+60=0

a = -1; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-1)·60
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-1}=\frac{0-4\sqrt{15}}{-2}
=-\frac{4\sqrt{15}}{-2}
=-\frac{2\sqrt{15}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-1}=\frac{0+4\sqrt{15}}{-2}
=\frac{4\sqrt{15}}{-2}
=\frac{2\sqrt{15}}{-1}
$