45=-q(-q+6)

Solution for 45=-q(-q+6) equation:

45=-q(-q+6)

We move all terms to the left:

45-(-q(-q+6))=0

We add all the numbers together, and all the variables

-(-q(-1q+6))+45=0


We calculate terms in parentheses: -(-q(-1q+6)), so:

-q(-1q+6)

We multiply parentheses

1q^2-6q

We add all the numbers together, and all the variables

q^2-6q

Back to the equation:

-(q^2-6q)


We get rid of parentheses

-q^2+6q+45=0

We add all the numbers together, and all the variables

-1q^2+6q+45=0

a = -1; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-1)·45
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*-1}=\frac{-6-6\sqrt{6}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*-1}=\frac{-6+6\sqrt{6}}{-2}
$