81=6b^2+57

Solution for 81=6b^2+57 equation:

81=6b^2+57

We move all terms to the left:

81-(6b^2+57)=0

We get rid of parentheses

-6b^2-57+81=0

We add all the numbers together, and all the variables

-6b^2+24=0

a = -6; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-6)·24
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-6}=\frac{-24}{-12}
=+2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-6}=\frac{24}{-12}
=-2
$