27=-a(a+5)+6(a+8)

Solution for 27=-a(a+5)+6(a+8) equation:

27=-a(a+5)+6(a+8)

We move all terms to the left:

27-(-a(a+5)+6(a+8))=0


We calculate terms in parentheses: -(-a(a+5)+6(a+8)), so:

-a(a+5)+6(a+8)

We multiply parentheses

-a^2-5a+6a+48

We add all the numbers together, and all the variables

-1a^2+a+48

Back to the equation:

-(-1a^2+a+48)


We get rid of parentheses

1a^2-a-48+27=0

We add all the numbers together, and all the variables

a^2-1a-21=0

a = 1; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·1·(-21)
Δ = 85
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{-(-1)-\sqrt{85}}{2*1}=\frac{1-\sqrt{85}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*1}=\frac{1+\sqrt{85}}{2}
$