27=b(b-6)

Solution for 27=b(b-6) equation:

27=b(b-6)

We move all terms to the left:

27-(b(b-6))=0


We calculate terms in parentheses: -(b(b-6)), so:

b(b-6)

We multiply parentheses

b^2-6b

Back to the equation:

-(b^2-6b)


We get rid of parentheses

-b^2+6b+27=0

We add all the numbers together, and all the variables

-1b^2+6b+27=0

a = -1; b = 6; c = +27;
Δ = b2-4ac
Δ = 62-4·(-1)·27
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-1}=\frac{-18}{-2}
=+9
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-1}=\frac{6}{-2}
=-3
$